Introduction

Welcome to the Time Door API documentation. Time Door is a time series analysis REST API. It receives JSON-encoded time series data, performs statistical computations, and returns JSON-encoded results.

https://api.timedoor.io

API base URL

Meta

The key words must, must not, required, shall, shall not, should, should not, recommended, may, and optional in this document are to be interpreted as described in RFC 2119.

Variable naming

All variables are named according to the snake_case naming convention.

Timeout

All endpoints terminate after 60 seconds.

Time series data

Uppercase N refers to the number of time series, lowercase n refers to the number of observations in a time series.

Format

Dates and times must be represented as described in RFC 3339, section 5.6, a subset of the ISO8601 date and time format.

"2019-04-12T23:20:50Z"
"2019-04-12T23:20:50.452Z"
"2019-12-19T16:39:57-08:00"

Valid date and time format examples

Assumptions

All time series analysis algorithms assume that the time series data is equidistant (evenly spaced in time).

Time index mapping

Time Door uses complete 1:1 time index mapping between input and output data for time-based statistics.

Authentication

Authentication to the Time Door API is performed by providing a custom authentication header named X-Time-Door-Key.

X-Time-Door-Key: 7589649-JUST-A-RANDOM-KEY

Authentication header example

Errors

Time Door uses standard HTTP status codes to indicate the success or failure of an API request.

200 OK Request completed successfully.
400 Bad Request The request is invalid, often due to missing a required parameter or invalid JSON.
401 Unauthorized No valid API key provided.
404 Not Found The requested resource or route does not exist.
500 Internal Server Error Something went wrong on our side.
504 Gateway Timeout Computation duration exceeded the maximum of 60 seconds.

Recommendations

The following recommendations for data transformation arguments for parametric and nonparametric algorithms are very general. The specifics of your use case may suggest other arguments.

For nonparametric algorithms, it is recommended to use the default data transformation arguments (all apply values set to false).

For parametric algorithms and no prior knowledge about the stationarity of the data, it is recommended to set the apply values for box_cox, seasonal_diff and first_diff to true and set lambda and n_diffs to auto.

For parametric algorithms that use fast, non-stationary data, it is recommended not to use auto values for the data transformation arguments. This optimizes for speed, consistent data transformations and error prevention. It is also recommended to set the reproduction argument to false (default) to reduce the size of the returned data.

{
  "box_cox": {
    "apply": false
  },
  "log": {
    "apply": false
  },
  "seasonal_diff": {
    "apply": false
  },
  "first_diff": {
    "apply": false
  }
}

Recommended transformation arguments for nonparametric algorithms.

{
  "box_cox": {
    "apply": true,
    "lambda": "auto"
  },
  "log": {
    "apply": false
  },
  "seasonal_diff": {
    "apply": true,
    "n_diffs": "auto"
  },
  "first_diff": {
    "apply": true,
    "n_diffs": "auto"
  }
}

Recommended transformation arguments for parametric algorithms.

{
  "box_cox": {
    "apply": false
  },
  "log": {
    "apply": false
  },
  "seasonal_diff": {
    "apply": false
  },
  "first_diff": {
    "apply": true,
    "n_diffs": 1
  }
}

Recommended transformation arguments example for using fast, non-stationary data with parametric algorithms. Note that no automatic transformations are being performed.

Endpoints

The endpoints of the Time Door API strive to provide accessibility, integration and transparency.

Accessibility

Every endpoint receives only one required argument (the time series data) and provides working example requests – making it easy to get started with our API.

Integration

Every endpoint provides advanced value imputation methods to replace missing values.

Every endpoint provides (automatic) data transformations prior to the main analysis to deliver valid results.

Transparency

If the reproduction argument is set to true, each response contains the applied arguments, every imputed missing value and every applied data transformation – enabling full reproducibility of the results.

Time series data

if missing values

Missing value imputation

if unfulfilled data assumptions

Data transformations

Statistical computation

f(x)

Results

if reproduction

Applied arguments

if missing values

Imputed values

Applied data transformations

Statistical computation results

auto ARIMA

POST /invocation/auto-arima

Forecasting
univariate | nonparametric

Automatic univariate time series forecasting with ARIMA models.

ARGUMENTS

time_series
REQUIREDarray(length: 1)

An array of objects, each representing 1 distinct time series.

reproduction
optionalbooleandefault: false

Return imputed values, applied data transformations and arguments. Useful for reproduction of the results.

precision
optionalobject

Decimal point precision of the output data.

stepwise
optionalbooleandefault: true

Set stepwise and approximation to true for fast model search and to false for best results.

approximation
optionalbooleandefault: true

Set stepwise and approximation to true for fast model search and to false for best results.

non_stationary
optionalbooleandefault: true

Include non-stationary models in search.

seasonal
optionalbooleandefault: true

Include non-stationary models in search.

ic
optionalstringdefault: aicc
valid values: aicc, aic, bic

Information criterion used for model selection.

box_cox_lambda
optionalnull | string | numbermin: -1max: 2

If null, the Box-Cox transformation is not applied.

If valid number, the Box-Cox transformation with the lambda parameter given by the box_cox_lambda argument is applied.

If auto, the optimal lambda transformation parameter is determined based on Guerrero's (1993) method and the Box-Cox transformation with the automatically determined lambda parameter is applied to the time series data.

bias_adj
optionalbooleandefault: false

If true adjusted back-transformed mean for Box-Cox transformations is used. If false median forecasts are produced. Argument ignored if box_cox_lambda = null.

unit_root_test
optionalstringdefault: kpss
valid values: kpss, adf, pp

kpss = Kwiatkowski-Phillips-Schmidt-Shin (1992) test, adf = Augmented Dickey-Fuller (1979) test, pp = Phillips-Perron (1988) test.

seasonal_test
optionalstringdefault: ss
valid values: ss, ch, hegy, ocsb

ss = Seasonal Strength (Wang et al., 2006), ch = Canova-Hansen (1995) test, hegy = Hylleberg-Engle-Granger-Yoo (1990) test, ocsb = Osborn-Chui-Smith-Birchenhall (1988) test.

alpha
optionalnumberdefault: 0.05min: 0.01max: 0.1

The statistical significance level of the stationarity and seasonality tests.

ci_level
optionalintegerdefault: 95min: 80max: 99

The confidence interval (%).

horizon
optionalintegerdefault: 10min: 1

The forecast horizon length.

RETURNS

{
  "stepwise": true,
  "approximation": true,
  "non_stationary": true,
  "seasonal": true,
  "ic": "aicc",
  "box_cox_lambda": null,
  "bias_adj": false,
  "unit_root_test": "kpss",
  "seasonal_test": "ss",
  "alpha": 0.05,
  "ci_level": 95,
  "horizon": 10,
  "reproduction": false,
  "precision": {
    "digits": 4,
    "method": "significant"
  },
  "time_series": [
    {
      "data": {
        "2020-01-01T00:00:00Z": 28.0137,
        "2020-01-01T00:00:01Z": 27.8591,
        "2020-01-01T00:00:02Z": 27.6281,
        "2020-01-01T00:00:03Z": 27.0703,
        "2020-01-01T00:00:04Z": 25.7454,
        "2020-01-01T00:00:05Z": 27.0635,
        "2020-01-01T00:00:06Z": 27.9731,
        "2020-01-01T00:00:07Z": 28.1618,
        "2020-01-01T00:00:08Z": 29.5978,
        "2020-01-01T00:00:09Z": 30.9978,
        "2020-01-01T00:00:10Z": 31.0237,
        "2020-01-01T00:00:11Z": 31.6535,
        "2020-01-01T00:00:12Z": 32.0346,
        "2020-01-01T00:00:13Z": 31.8492,
        "2020-01-01T00:00:14Z": 32.3419,
        "2020-01-01T00:00:15Z": 32.0351,
        "2020-01-01T00:00:16Z": 30.7687,
        "2020-01-01T00:00:17Z": 30.374,
        "2020-01-01T00:00:18Z": 28.1942,
        "2020-01-01T00:00:19Z": 25.9453,
        "2020-01-01T00:00:20Z": 23.6843,
        "2020-01-01T00:00:21Z": 21.943,
        "2020-01-01T00:00:22Z": 20.309,
        "2020-01-01T00:00:23Z": 19.3427,
        "2020-01-01T00:00:24Z": 19.3478,
        "2020-01-01T00:00:25Z": 19.7972,
        "2020-01-01T00:00:26Z": 21.2299,
        "2020-01-01T00:00:27Z": 22.4813,
        "2020-01-01T00:00:28Z": 23.2128,
        "2020-01-01T00:00:29Z": 22.7081,
        "2020-01-01T00:00:30Z": 23.1786,
        "2020-01-01T00:00:31Z": 22.805,
        "2020-01-01T00:00:32Z": 23.4281,
        "2020-01-01T00:00:33Z": 24.5025,
        "2020-01-01T00:00:34Z": 24.213,
        "2020-01-01T00:00:35Z": 23.3072,
        "2020-01-01T00:00:36Z": 23.7229,
        "2020-01-01T00:00:37Z": 23.1353,
        "2020-01-01T00:00:38Z": 24.0197,
        "2020-01-01T00:00:39Z": 23.3354,
        "2020-01-01T00:00:40Z": 24.171,
        "2020-01-01T00:00:41Z": 23.8188,
        "2020-01-01T00:00:42Z": 24.6172,
        "2020-01-01T00:00:43Z": 24.2777,
        "2020-01-01T00:00:44Z": 24.2283,
        "2020-01-01T00:00:45Z": 25.1955,
        "2020-01-01T00:00:46Z": 26.4958,
        "2020-01-01T00:00:47Z": 28.3069,
        "2020-01-01T00:00:48Z": 29.7687,
        "2020-01-01T00:00:49Z": 30.9865,
        "2020-01-01T00:00:50Z": 29.7695,
        "2020-01-01T00:00:51Z": 30.1204,
        "2020-01-01T00:00:52Z": 31.742,
        "2020-01-01T00:00:53Z": 34.6089,
        "2020-01-01T00:00:54Z": 36.054,
        "2020-01-01T00:00:55Z": 36.3756,
        "2020-01-01T00:00:56Z": 37.36,
        "2020-01-01T00:00:57Z": 38.1193,
        "2020-01-01T00:00:58Z": 38.5563,
        "2020-01-01T00:00:59Z": 40.6662,
        "2020-01-01T00:01:00Z": 42.6862,
        "2020-01-01T00:01:01Z": 45.0665,
        "2020-01-01T00:01:02Z": 46.3616,
        "2020-01-01T00:01:03Z": 46.8506,
        "2020-01-01T00:01:04Z": 47.7675,
        "2020-01-01T00:01:05Z": 47.6054,
        "2020-01-01T00:01:06Z": 46.2565,
        "2020-01-01T00:01:07Z": 45.536,
        "2020-01-01T00:01:08Z": 46.3415,
        "2020-01-01T00:01:09Z": 48.0423,
        "2020-01-01T00:01:10Z": 50.8812,
        "2020-01-01T00:01:11Z": 52.6965,
        "2020-01-01T00:01:12Z": 54.7823,
        "2020-01-01T00:01:13Z": 53.512,
        "2020-01-01T00:01:14Z": 53.2565,
        "2020-01-01T00:01:15Z": 53.0911,
        "2020-01-01T00:01:16Z": 52.4152,
        "2020-01-01T00:01:17Z": 51.8234,
        "2020-01-01T00:01:18Z": 50.2512,
        "2020-01-01T00:01:19Z": 51.0036,
        "2020-01-01T00:01:20Z": 51.9257,
        "2020-01-01T00:01:21Z": 52.5759,
        "2020-01-01T00:01:22Z": 54.1171,
        "2020-01-01T00:01:23Z": 55.4398,
        "2020-01-01T00:01:24Z": 55.5233,
        "2020-01-01T00:01:25Z": 53.8893,
        "2020-01-01T00:01:26Z": 52.8306,
        "2020-01-01T00:01:27Z": 52.2715,
        "2020-01-01T00:01:28Z": 51.0688,
        "2020-01-01T00:01:29Z": 51.6046,
        "2020-01-01T00:01:30Z": 51.6625,
        "2020-01-01T00:01:31Z": 51.1545,
        "2020-01-01T00:01:32Z": 50.4331,
        "2020-01-01T00:01:33Z": 49.8225,
        "2020-01-01T00:01:34Z": 47.5345,
        "2020-01-01T00:01:35Z": 48.5842,
        "2020-01-01T00:01:36Z": 49.3886,
        "2020-01-01T00:01:37Z": 50.4767,
        "2020-01-01T00:01:38Z": 49.5141,
        "2020-01-01T00:01:39Z": 50.3534
      },
      "imputation": {
        "method": "linear",
        "ma_window_size": 10
      }
    }
  ]
}
{
  "report": {
    "computation_time": 1026.48
  },
  "result": {
    "reproduction": {},
    "data": {
      "order": {
        "p": 1,
        "d": 1,
        "q": 0,
        "P": 0,
        "D": 0,
        "Q": 0,
        "period": null
      },
      "forecast": [
        {
          "t": 1,
          "mean": 50.81,
          "upper": 52.74,
          "lower": 48.87
        },
        {
          "t": 2,
          "mean": 51.05,
          "upper": 54.61,
          "lower": 47.5
        },
        {
          "t": 3,
          "mean": 51.19,
          "upper": 56.21,
          "lower": 46.16
        },
        {
          "t": 4,
          "mean": 51.26,
          "upper": 57.6,
          "lower": 44.93
        },
        {
          "t": 5,
          "mean": 51.3,
          "upper": 58.81,
          "lower": 43.79
        },
        {
          "t": 6,
          "mean": 51.32,
          "upper": 59.88,
          "lower": 42.76
        },
        {
          "t": 7,
          "mean": 51.33,
          "upper": 60.85,
          "lower": 41.81
        },
        {
          "t": 8,
          "mean": 51.34,
          "upper": 61.74,
          "lower": 40.94
        },
        {
          "t": 9,
          "mean": 51.34,
          "upper": 62.56,
          "lower": 40.12
        },
        {
          "t": 10,
          "mean": 51.34,
          "upper": 63.33,
          "lower": 39.36
        }
      ],
      "sigma^2": 0.9738,
      "aic": 281.7,
      "aicc": 281.8,
      "bic": 286.9,
      "box_cox_lambda": null
    }
  }
}
{
  "report": {
    "computation_time": 1026.48
  },
  "result": {
    "reproduction": {},
    "data": {
      "order": {
        "p": 1,
        "d": 1,
        "q": 0,
        "P": 0,
        "D": 0,
        "Q": 0,
        "period": null
      },
      "forecast": [
        {
          "t": 1,
          "mean": 50.81,
          "upper": 52.74,
          "lower": 48.87
        },
        {
          "t": 2,
          "mean": 51.05,
          "upper": 54.61,
          "lower": 47.5
        },
        {
          "t": 3,
          "mean": 51.19,
          "upper": 56.21,
          "lower": 46.16
        },
        {
          "t": 4,
          "mean": 51.26,
          "upper": 57.6,
          "lower": 44.93
        },
        {
          "t": 5,
          "mean": 51.3,
          "upper": 58.81,
          "lower": 43.79
        },
        {
          "t": 6,
          "mean": 51.32,
          "upper": 59.88,
          "lower": 42.76
        },
        {
          "t": 7,
          "mean": 51.33,
          "upper": 60.85,
          "lower": 41.81
        },
        {
          "t": 8,
          "mean": 51.34,
          "upper": 61.74,
          "lower": 40.94
        },
        {
          "t": 9,
          "mean": 51.34,
          "upper": 62.56,
          "lower": 40.12
        },
        {
          "t": 10,
          "mean": 51.34,
          "upper": 63.33,
          "lower": 39.36
        }
      ],
      "sigma^2": 0.9738,
      "aic": 281.7,
      "aicc": 281.8,
      "bic": 286.9,
      "box_cox_lambda": null
    }
  }
}
        

changepoint detection

POST /invocation/changepoint-detection

Changepoint detection
univariate | nonparametric

Detects multiple changepoints in the time series data using the changepoint detection algorithm Pruned Exact Linear Time (PELT) with a nonparametric cost function based on the empirical distribution of the data. PELT applies a penalty to prevent under- or over-fitting.

ARGUMENTS

time_series
REQUIREDarray(length: 1)

An array of objects, each representing 1 distinct time series.

reproduction
optionalbooleandefault: false

Return imputed values, applied data transformations and arguments. Useful for reproduction of the results.

precision
optionalobject

Decimal point precision of the output data.

penalty
optionalstringdefault: mbic
valid values: aic, bic, mbic, sic, hannan_quinn

The penalty to prevent under- or over-fitting.

min_distance
optionalintegerdefault: 1min: 1

Minimum distance between changepoints. Changed to min_distance = floor(n/2), if min_distance > n/2.

RETURNS

{
  "penalty": "mbic",
  "min_distance": 1,
  "reproduction": false,
  "precision": {
    "digits": 4,
    "method": "significant"
  },
  "time_series": [
    {
      "data": {
        "2020-01-01T00:00:00Z": 28.0137,
        "2020-01-01T00:00:01Z": 27.8591,
        "2020-01-01T00:00:02Z": 27.6281,
        "2020-01-01T00:00:03Z": 27.0703,
        "2020-01-01T00:00:04Z": 25.7454,
        "2020-01-01T00:00:05Z": 27.0635,
        "2020-01-01T00:00:06Z": 27.9731,
        "2020-01-01T00:00:07Z": 28.1618,
        "2020-01-01T00:00:08Z": 29.5978,
        "2020-01-01T00:00:09Z": 30.9978,
        "2020-01-01T00:00:10Z": 31.0237,
        "2020-01-01T00:00:11Z": 31.6535,
        "2020-01-01T00:00:12Z": 32.0346,
        "2020-01-01T00:00:13Z": 31.8492,
        "2020-01-01T00:00:14Z": 32.3419,
        "2020-01-01T00:00:15Z": 32.0351,
        "2020-01-01T00:00:16Z": 30.7687,
        "2020-01-01T00:00:17Z": 30.374,
        "2020-01-01T00:00:18Z": 28.1942,
        "2020-01-01T00:00:19Z": 25.9453,
        "2020-01-01T00:00:20Z": 23.6843,
        "2020-01-01T00:00:21Z": 21.943,
        "2020-01-01T00:00:22Z": 20.309,
        "2020-01-01T00:00:23Z": 19.3427,
        "2020-01-01T00:00:24Z": 19.3478,
        "2020-01-01T00:00:25Z": 19.7972,
        "2020-01-01T00:00:26Z": 21.2299,
        "2020-01-01T00:00:27Z": 22.4813,
        "2020-01-01T00:00:28Z": 23.2128,
        "2020-01-01T00:00:29Z": 22.7081,
        "2020-01-01T00:00:30Z": 23.1786,
        "2020-01-01T00:00:31Z": 22.805,
        "2020-01-01T00:00:32Z": 23.4281,
        "2020-01-01T00:00:33Z": 24.5025,
        "2020-01-01T00:00:34Z": 24.213,
        "2020-01-01T00:00:35Z": 23.3072,
        "2020-01-01T00:00:36Z": 23.7229,
        "2020-01-01T00:00:37Z": 23.1353,
        "2020-01-01T00:00:38Z": 24.0197,
        "2020-01-01T00:00:39Z": 23.3354,
        "2020-01-01T00:00:40Z": 24.171,
        "2020-01-01T00:00:41Z": 23.8188,
        "2020-01-01T00:00:42Z": 24.6172,
        "2020-01-01T00:00:43Z": 24.2777,
        "2020-01-01T00:00:44Z": 24.2283,
        "2020-01-01T00:00:45Z": 25.1955,
        "2020-01-01T00:00:46Z": 26.4958,
        "2020-01-01T00:00:47Z": 28.3069,
        "2020-01-01T00:00:48Z": 29.7687,
        "2020-01-01T00:00:49Z": 30.9865,
        "2020-01-01T00:00:50Z": 29.7695,
        "2020-01-01T00:00:51Z": 30.1204,
        "2020-01-01T00:00:52Z": 31.742,
        "2020-01-01T00:00:53Z": 34.6089,
        "2020-01-01T00:00:54Z": 36.054,
        "2020-01-01T00:00:55Z": 36.3756,
        "2020-01-01T00:00:56Z": 37.36,
        "2020-01-01T00:00:57Z": 38.1193,
        "2020-01-01T00:00:58Z": 38.5563,
        "2020-01-01T00:00:59Z": 40.6662,
        "2020-01-01T00:01:00Z": 42.6862,
        "2020-01-01T00:01:01Z": 45.0665,
        "2020-01-01T00:01:02Z": 46.3616,
        "2020-01-01T00:01:03Z": 46.8506,
        "2020-01-01T00:01:04Z": 47.7675,
        "2020-01-01T00:01:05Z": 47.6054,
        "2020-01-01T00:01:06Z": 46.2565,
        "2020-01-01T00:01:07Z": 45.536,
        "2020-01-01T00:01:08Z": 46.3415,
        "2020-01-01T00:01:09Z": 48.0423,
        "2020-01-01T00:01:10Z": 50.8812,
        "2020-01-01T00:01:11Z": 52.6965,
        "2020-01-01T00:01:12Z": 54.7823,
        "2020-01-01T00:01:13Z": 53.512,
        "2020-01-01T00:01:14Z": 53.2565,
        "2020-01-01T00:01:15Z": 53.0911,
        "2020-01-01T00:01:16Z": 52.4152,
        "2020-01-01T00:01:17Z": 51.8234,
        "2020-01-01T00:01:18Z": 50.2512,
        "2020-01-01T00:01:19Z": 51.0036,
        "2020-01-01T00:01:20Z": 51.9257,
        "2020-01-01T00:01:21Z": 52.5759,
        "2020-01-01T00:01:22Z": 54.1171,
        "2020-01-01T00:01:23Z": 55.4398,
        "2020-01-01T00:01:24Z": 55.5233,
        "2020-01-01T00:01:25Z": 53.8893,
        "2020-01-01T00:01:26Z": 52.8306,
        "2020-01-01T00:01:27Z": 52.2715,
        "2020-01-01T00:01:28Z": 51.0688,
        "2020-01-01T00:01:29Z": 51.6046,
        "2020-01-01T00:01:30Z": 51.6625,
        "2020-01-01T00:01:31Z": 51.1545,
        "2020-01-01T00:01:32Z": 50.4331,
        "2020-01-01T00:01:33Z": 49.8225,
        "2020-01-01T00:01:34Z": 47.5345,
        "2020-01-01T00:01:35Z": 48.5842,
        "2020-01-01T00:01:36Z": 49.3886,
        "2020-01-01T00:01:37Z": 50.4767,
        "2020-01-01T00:01:38Z": 49.5141,
        "2020-01-01T00:01:39Z": 50.3534
      },
      "imputation": {
        "method": "linear",
        "ma_window_size": 10
      },
      "transformations": {
        "box_cox": {
          "apply": false,
          "lambda": "auto",
          "method": "guerrero",
          "upper": 2,
          "lower": -1
        },
        "log": {
          "apply": false,
          "base": "e",
          "factor": null,
          "constant": 1
        },
        "seasonal_diff": {
          "apply": false,
          "period": "auto",
          "n_diffs": "auto",
          "test": "ss",
          "alpha": 0.05
        },
        "first_diff": {
          "apply": false,
          "n_diffs": "auto",
          "test": "kpss",
          "type": "level",
          "alpha": 0.05
        }
      }
    }
  ]
}
{
  "report": {
    "computation_time": 467.35
  },
  "result": {
    "reproduction": {},
    "data": [
      "2020-01-01T00:00:19Z",
      "2020-01-01T00:00:27Z",
      "2020-01-01T00:00:47Z",
      "2020-01-01T00:01:09Z",
      "2020-01-01T00:01:27Z",
      "2020-01-01T00:01:39Z"
    ]
  }
}
{
  "report": {
    "computation_time": 467.35
  },
  "result": {
    "reproduction": {},
    "data": [
      "2020-01-01T00:00:19Z",
      "2020-01-01T00:00:27Z",
      "2020-01-01T00:00:47Z",
      "2020-01-01T00:01:09Z",
      "2020-01-01T00:01:27Z",
      "2020-01-01T00:01:39Z"
    ]
  }
}
        

collective and point anomalies

POST /invocation/collective-and-point-anomalies

Anomaly detection
univariate | parametric

Collective And Point Anomalies (CAPA) is an algorithm for detecting collective anomalies identified by a change in mean, variance, or both, and differentiating them from point anomalies.

ARGUMENTS

time_series
REQUIREDarray(length: 1)

An array of objects, each representing 1 distinct time series.

reproduction
optionalbooleandefault: false

Return imputed values, applied data transformations and arguments. Useful for reproduction of the results.

precision
optionalobject

Decimal point precision of the output data.

method
optionalstringdefault: mean_var
valid values: mean_var, mean

mean_var detects collective anomalies identified by joint changes in mean and variance. mean detects collective anomalies identified by changes in mean only.

min_ca_size
optionalintegerdefault: 10min: 3

The minimum size of collective anomalies in number of data points to be considered as such. Changed to min_ca_size = floor(n/2), if min_ca_size > n/2.

RETURNS

{
  "method": "mean_var",
  "min_ca_size": 10,
  "reproduction": false,
  "precision": {
    "digits": 4,
    "method": "significant"
  },
  "time_series": [
    {
      "data": {
        "2020-01-01T00:00:00Z": 28.0137,
        "2020-01-01T00:00:01Z": 27.8591,
        "2020-01-01T00:00:02Z": 27.6281,
        "2020-01-01T00:00:03Z": 27.0703,
        "2020-01-01T00:00:04Z": 25.7454,
        "2020-01-01T00:00:05Z": 27.0635,
        "2020-01-01T00:00:06Z": 27.9731,
        "2020-01-01T00:00:07Z": 28.1618,
        "2020-01-01T00:00:08Z": 29.5978,
        "2020-01-01T00:00:09Z": 30.9978,
        "2020-01-01T00:00:10Z": 31.0237,
        "2020-01-01T00:00:11Z": 31.6535,
        "2020-01-01T00:00:12Z": 32.0346,
        "2020-01-01T00:00:13Z": 31.8492,
        "2020-01-01T00:00:14Z": 32.3419,
        "2020-01-01T00:00:15Z": 32.0351,
        "2020-01-01T00:00:16Z": 30.7687,
        "2020-01-01T00:00:17Z": 30.374,
        "2020-01-01T00:00:18Z": 28.1942,
        "2020-01-01T00:00:19Z": 25.9453,
        "2020-01-01T00:00:20Z": 23.6843,
        "2020-01-01T00:00:21Z": 21.943,
        "2020-01-01T00:00:22Z": 20.309,
        "2020-01-01T00:00:23Z": 19.3427,
        "2020-01-01T00:00:24Z": 19.3478,
        "2020-01-01T00:00:25Z": 19.7972,
        "2020-01-01T00:00:26Z": 21.2299,
        "2020-01-01T00:00:27Z": 22.4813,
        "2020-01-01T00:00:28Z": 23.2128,
        "2020-01-01T00:00:29Z": 22.7081,
        "2020-01-01T00:00:30Z": 23.1786,
        "2020-01-01T00:00:31Z": 22.805,
        "2020-01-01T00:00:32Z": 23.4281,
        "2020-01-01T00:00:33Z": 24.5025,
        "2020-01-01T00:00:34Z": 24.213,
        "2020-01-01T00:00:35Z": 23.3072,
        "2020-01-01T00:00:36Z": 23.7229,
        "2020-01-01T00:00:37Z": 23.1353,
        "2020-01-01T00:00:38Z": 24.0197,
        "2020-01-01T00:00:39Z": 23.3354,
        "2020-01-01T00:00:40Z": 24.171,
        "2020-01-01T00:00:41Z": 23.8188,
        "2020-01-01T00:00:42Z": 24.6172,
        "2020-01-01T00:00:43Z": 24.2777,
        "2020-01-01T00:00:44Z": 24.2283,
        "2020-01-01T00:00:45Z": 25.1955,
        "2020-01-01T00:00:46Z": 26.4958,
        "2020-01-01T00:00:47Z": 28.3069,
        "2020-01-01T00:00:48Z": 29.7687,
        "2020-01-01T00:00:49Z": 30.9865,
        "2020-01-01T00:00:50Z": 29.7695,
        "2020-01-01T00:00:51Z": 30.1204,
        "2020-01-01T00:00:52Z": 31.742,
        "2020-01-01T00:00:53Z": 34.6089,
        "2020-01-01T00:00:54Z": 36.054,
        "2020-01-01T00:00:55Z": 36.3756,
        "2020-01-01T00:00:56Z": 37.36,
        "2020-01-01T00:00:57Z": 38.1193,
        "2020-01-01T00:00:58Z": 38.5563,
        "2020-01-01T00:00:59Z": 40.6662,
        "2020-01-01T00:01:00Z": 42.6862,
        "2020-01-01T00:01:01Z": 45.0665,
        "2020-01-01T00:01:02Z": 46.3616,
        "2020-01-01T00:01:03Z": 46.8506,
        "2020-01-01T00:01:04Z": 47.7675,
        "2020-01-01T00:01:05Z": 47.6054,
        "2020-01-01T00:01:06Z": 46.2565,
        "2020-01-01T00:01:07Z": 45.536,
        "2020-01-01T00:01:08Z": 46.3415,
        "2020-01-01T00:01:09Z": 48.0423,
        "2020-01-01T00:01:10Z": 50.8812,
        "2020-01-01T00:01:11Z": 52.6965,
        "2020-01-01T00:01:12Z": 54.7823,
        "2020-01-01T00:01:13Z": 53.512,
        "2020-01-01T00:01:14Z": 53.2565,
        "2020-01-01T00:01:15Z": 53.0911,
        "2020-01-01T00:01:16Z": 52.4152,
        "2020-01-01T00:01:17Z": 51.8234,
        "2020-01-01T00:01:18Z": 50.2512,
        "2020-01-01T00:01:19Z": 51.0036,
        "2020-01-01T00:01:20Z": 51.9257,
        "2020-01-01T00:01:21Z": 52.5759,
        "2020-01-01T00:01:22Z": 54.1171,
        "2020-01-01T00:01:23Z": 55.4398,
        "2020-01-01T00:01:24Z": 55.5233,
        "2020-01-01T00:01:25Z": 53.8893,
        "2020-01-01T00:01:26Z": 52.8306,
        "2020-01-01T00:01:27Z": 52.2715,
        "2020-01-01T00:01:28Z": 51.0688,
        "2020-01-01T00:01:29Z": 51.6046,
        "2020-01-01T00:01:30Z": 51.6625,
        "2020-01-01T00:01:31Z": 51.1545,
        "2020-01-01T00:01:32Z": 50.4331,
        "2020-01-01T00:01:33Z": 49.8225,
        "2020-01-01T00:01:34Z": 47.5345,
        "2020-01-01T00:01:35Z": 48.5842,
        "2020-01-01T00:01:36Z": 49.3886,
        "2020-01-01T00:01:37Z": 50.4767,
        "2020-01-01T00:01:38Z": 49.5141,
        "2020-01-01T00:01:39Z": 50.3534
      },
      "imputation": {
        "method": "linear",
        "ma_window_size": 10
      },
      "transformations": {
        "box_cox": {
          "apply": false,
          "lambda": "auto",
          "method": "guerrero",
          "upper": 2,
          "lower": -1
        },
        "log": {
          "apply": false,
          "base": "e",
          "factor": null,
          "constant": 1
        },
        "seasonal_diff": {
          "apply": false,
          "period": "auto",
          "n_diffs": "auto",
          "test": "ss",
          "alpha": 0.05
        },
        "first_diff": {
          "apply": true,
          "n_diffs": 1,
          "test": "kpss",
          "type": "level",
          "alpha": 0.05
        }
      }
    }
  ]
}
{
  "report": {
    "computation_time": 343.56
  },
  "result": {
    "reproduction": {},
    "data": {
      "collective_anomalies": [
        {
          "t": "2020-01-01T00:00:15Z",
          "mean_change_strength": 2.57,
          "variance_change_strength": 0.1752,
          "size": 10
        }
      ],
      "point_anomalies": []
    }
  }
}
{
  "report": {
    "computation_time": 343.56
  },
  "result": {
    "reproduction": {},
    "data": {
      "collective_anomalies": [
        {
          "t": "2020-01-01T00:00:15Z",
          "mean_change_strength": 2.57,
          "variance_change_strength": 0.1752,
          "size": 10
        }
      ],
      "point_anomalies": []
    }
  }
}
        

conditional heteroskedasticity

POST /invocation/conditional-heteroskedasticity

Early warning signal detection
univariate | nonparametric | fast data

Estimates conditional heteroskedasticity within a moving window along the time series by fitting an autoregressive model using AIC optimization. Conditional heteroskedasticity is associated with the dynamical phenomena of rising variability and flickering. Conditional heteroskedasticity signifies variance with a positive relationship with variance at previous time steps. Given that variability tends to increase prior to a phase transition, conditional heteroskedasticity can serve as an early indicator since the part of a time series near an impending shift appears as a high variability cluster, while the part of the time series that moves away from the shift appears as a low variability cluster.

ARGUMENTS

time_series
REQUIREDarray(length: 1)

An array of objects, each representing 1 distinct time series.

reproduction
optionalbooleandefault: false

Return imputed values, applied data transformations and arguments. Useful for reproduction of the results.

precision
optionalobject

Decimal point precision of the output data.

alpha
optionalnumberdefault: 0.05min: 0.01max: 0.1

The statistical significance level of the test.

window_size
optionalintegerdefault: 10min: 10

The size of the moving window in number of data points. Changed to window_size = floor(n/2), if window_size > n/2.

RETURNS

{
  "alpha": 0.05,
  "window_size": 10,
  "reproduction": false,
  "precision": {
    "digits": 4,
    "method": "significant"
  },
  "time_series": [
    {
      "data": {
        "2020-01-01T00:00:00Z": 28.0137,
        "2020-01-01T00:00:01Z": 27.8591,
        "2020-01-01T00:00:02Z": 27.6281,
        "2020-01-01T00:00:03Z": 27.0703,
        "2020-01-01T00:00:04Z": 25.7454,
        "2020-01-01T00:00:05Z": 27.0635,
        "2020-01-01T00:00:06Z": 27.9731,
        "2020-01-01T00:00:07Z": 28.1618,
        "2020-01-01T00:00:08Z": 29.5978,
        "2020-01-01T00:00:09Z": 30.9978,
        "2020-01-01T00:00:10Z": 31.0237,
        "2020-01-01T00:00:11Z": 31.6535,
        "2020-01-01T00:00:12Z": 32.0346,
        "2020-01-01T00:00:13Z": 31.8492,
        "2020-01-01T00:00:14Z": 32.3419,
        "2020-01-01T00:00:15Z": 32.0351,
        "2020-01-01T00:00:16Z": 30.7687,
        "2020-01-01T00:00:17Z": 30.374,
        "2020-01-01T00:00:18Z": 28.1942,
        "2020-01-01T00:00:19Z": 25.9453,
        "2020-01-01T00:00:20Z": 23.6843,
        "2020-01-01T00:00:21Z": 21.943,
        "2020-01-01T00:00:22Z": 20.309,
        "2020-01-01T00:00:23Z": 19.3427,
        "2020-01-01T00:00:24Z": 19.3478,
        "2020-01-01T00:00:25Z": 19.7972,
        "2020-01-01T00:00:26Z": 21.2299,
        "2020-01-01T00:00:27Z": 22.4813,
        "2020-01-01T00:00:28Z": 23.2128,
        "2020-01-01T00:00:29Z": 22.7081,
        "2020-01-01T00:00:30Z": 23.1786,
        "2020-01-01T00:00:31Z": 22.805,
        "2020-01-01T00:00:32Z": 23.4281,
        "2020-01-01T00:00:33Z": 24.5025,
        "2020-01-01T00:00:34Z": 24.213,
        "2020-01-01T00:00:35Z": 23.3072,
        "2020-01-01T00:00:36Z": 23.7229,
        "2020-01-01T00:00:37Z": 23.1353,
        "2020-01-01T00:00:38Z": 24.0197,
        "2020-01-01T00:00:39Z": 23.3354,
        "2020-01-01T00:00:40Z": 24.171,
        "2020-01-01T00:00:41Z": 23.8188,
        "2020-01-01T00:00:42Z": 24.6172,
        "2020-01-01T00:00:43Z": 24.2777,
        "2020-01-01T00:00:44Z": 24.2283,
        "2020-01-01T00:00:45Z": 25.1955,
        "2020-01-01T00:00:46Z": 26.4958,
        "2020-01-01T00:00:47Z": 28.3069,
        "2020-01-01T00:00:48Z": 29.7687,
        "2020-01-01T00:00:49Z": 30.9865,
        "2020-01-01T00:00:50Z": 29.7695,
        "2020-01-01T00:00:51Z": 30.1204,
        "2020-01-01T00:00:52Z": 31.742,
        "2020-01-01T00:00:53Z": 34.6089,
        "2020-01-01T00:00:54Z": 36.054,
        "2020-01-01T00:00:55Z": 36.3756,
        "2020-01-01T00:00:56Z": 37.36,
        "2020-01-01T00:00:57Z": 38.1193,
        "2020-01-01T00:00:58Z": 38.5563,
        "2020-01-01T00:00:59Z": 40.6662,
        "2020-01-01T00:01:00Z": 42.6862,
        "2020-01-01T00:01:01Z": 45.0665,
        "2020-01-01T00:01:02Z": 46.3616,
        "2020-01-01T00:01:03Z": 46.8506,
        "2020-01-01T00:01:04Z": 47.7675,
        "2020-01-01T00:01:05Z": 47.6054,
        "2020-01-01T00:01:06Z": 46.2565,
        "2020-01-01T00:01:07Z": 45.536,
        "2020-01-01T00:01:08Z": 46.3415,
        "2020-01-01T00:01:09Z": 48.0423,
        "2020-01-01T00:01:10Z": 50.8812,
        "2020-01-01T00:01:11Z": 52.6965,
        "2020-01-01T00:01:12Z": 54.7823,
        "2020-01-01T00:01:13Z": 53.512,
        "2020-01-01T00:01:14Z": 53.2565,
        "2020-01-01T00:01:15Z": 53.0911,
        "2020-01-01T00:01:16Z": 52.4152,
        "2020-01-01T00:01:17Z": 51.8234,
        "2020-01-01T00:01:18Z": 50.2512,
        "2020-01-01T00:01:19Z": 51.0036,
        "2020-01-01T00:01:20Z": 51.9257,
        "2020-01-01T00:01:21Z": 52.5759,
        "2020-01-01T00:01:22Z": 54.1171,
        "2020-01-01T00:01:23Z": 55.4398,
        "2020-01-01T00:01:24Z": 55.5233,
        "2020-01-01T00:01:25Z": 53.8893,
        "2020-01-01T00:01:26Z": 52.8306,
        "2020-01-01T00:01:27Z": 52.2715,
        "2020-01-01T00:01:28Z": 51.0688,
        "2020-01-01T00:01:29Z": 51.6046,
        "2020-01-01T00:01:30Z": 51.6625,
        "2020-01-01T00:01:31Z": 51.1545,
        "2020-01-01T00:01:32Z": 50.4331,
        "2020-01-01T00:01:33Z": 49.8225,
        "2020-01-01T00:01:34Z": 47.5345,
        "2020-01-01T00:01:35Z": 48.5842,
        "2020-01-01T00:01:36Z": 49.3886,
        "2020-01-01T00:01:37Z": 50.4767,
        "2020-01-01T00:01:38Z": 49.5141,
        "2020-01-01T00:01:39Z": 50.3534
      },
      "imputation": {
        "method": "linear",
        "ma_window_size": 10
      },
      "transformations": {
        "box_cox": {
          "apply": false,
          "lambda": "auto",
          "method": "guerrero",
          "upper": 2,
          "lower": -1
        },
        "log": {
          "apply": false,
          "base": "e",
          "factor": null,
          "constant": 1
        },
        "seasonal_diff": {
          "apply": false,
          "period": "auto",
          "n_diffs": "auto",
          "test": "ss",
          "alpha": 0.05
        },
        "first_diff": {
          "apply": false,
          "n_diffs": "auto",
          "test": "kpss",
          "type": "level",
          "alpha": 0.05
        }
      }
    }
  ]
}
{
  "report": {
    "computation_time": 542.65
  },
  "result": {
    "reproduction": {},
    "data": [
      {
        "t": "2020-01-01T00:00:00Z",
        "r_squared": null,
        "critical_value": null,
        "ar_order": null
      },
      {
        "t": "2020-01-01T00:00:01Z",
        "r_squared": null,
        "critical_value": null,
        "ar_order": null
      },
      {
        "t": "2020-01-01T00:00:02Z",
        "r_squared": null,
        "critical_value": null,
        "ar_order": null
      },
      {
        "t": "2020-01-01T00:00:03Z",
        "r_squared": null,
        "critical_value": null,
        "ar_order": null
      },
      {
        "t": "2020-01-01T00:00:04Z",
        "r_squared": null,
        "critical_value": null,
        "ar_order": null
      },
      {
        "t": "2020-01-01T00:00:05Z",
        "r_squared": null,
        "critical_value": null,
        "ar_order": null
      },
      {
        "t": "2020-01-01T00:00:06Z",
        "r_squared": null,
        "critical_value": null,
        "ar_order": null
      },
      {
        "t": "2020-01-01T00:00:07Z",
        "r_squared": null,
        "critical_value": null,
        "ar_order": null
      },
      {
        "t": "2020-01-01T00:00:08Z",
        "r_squared": null,
        "critical_value": null,
        "ar_order": null
      },
      {
        "t": "2020-01-01T00:00:09Z",
        "r_squared": 0.06164,
        "critical_value": 0.4802,
        "ar_order": 1
      },
      {
        "t": "2020-01-01T00:00:10Z",
        "r_squared": 0.005787,
        "critical_value": 0.7683,
        "ar_order": 4
      },
      {
        "t": "2020-01-01T00:00:11Z",
        "r_squared": 0.0086,
        "critical_value": 0.7683,
        "ar_order": 4
      },
      {
        "t": "2020-01-01T00:00:12Z",
        "r_squared": 0.1503,
        "critical_value": 0.7683,
        "ar_order": 4
      },
      {
        "t": "2020-01-01T00:00:13Z",
        "r_squared": 0.4243,
        "critical_value": 0.7683,
        "ar_order": 4
      },
      {
        "t": "2020-01-01T00:00:14Z",
        "r_squared": 0.1287,
        "critical_value": 0.7683,
        "ar_order": 4
      },
      {
        "t": "2020-01-01T00:00:15Z",
        "r_squared": 0.1895,
        "critical_value": 0.7683,
        "ar_order": 4
      },
      {
        "t": "2020-01-01T00:00:16Z",
        "r_squared": 0.116,
        "critical_value": 0.7683,
        "ar_order": 4
      },
      {
        "t": "2020-01-01T00:00:17Z",
        "r_squared": 0.6102,
        "critical_value": 0.7683,
        "ar_order": 4
      },
      {
        "t": "2020-01-01T00:00:18Z",
        "r_squared": 0.02822,
        "critical_value": 0.7683,
        "ar_order": 4
      },
      {
        "t": "2020-01-01T00:00:19Z",
        "r_squared": 0.01888,
        "critical_value": 0.7683,
        "ar_order": 4
      },
      {
        "t": "2020-01-01T00:00:20Z",
        "r_squared": 0.01156,
        "critical_value": 0.7683,
        "ar_order": 4
      },
      {
        "t": "2020-01-01T00:00:21Z",
        "r_squared": 0.143,
        "critical_value": 0.7683,
        "ar_order": 4
      },
      {
        "t": "2020-01-01T00:00:22Z",
        "r_squared": 0.3208,
        "critical_value": 0.7683,
        "ar_order": 4
      },
      {
        "t": "2020-01-01T00:00:23Z",
        "r_squared": 0.04359,
        "critical_value": 0.7683,
        "ar_order": 4
      },
      {
        "t": "2020-01-01T00:00:24Z",
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        "t": "2020-01-01T00:00:54Z",
        "r_squared": 0.001717,
        "critical_value": 0.7683,
        "ar_order": 4
      },
      {
        "t": "2020-01-01T00:00:55Z",
        "r_squared": 0.01646,
        "critical_value": 0.7683,
        "ar_order": 4
      },
      {
        "t": "2020-01-01T00:00:56Z",
        "r_squared": 0.0007108,
        "critical_value": 0.7683,
        "ar_order": 4
      },
      {
        "t": "2020-01-01T00:00:57Z",
        "r_squared": 0.02199,
        "critical_value": 0.7683,
        "ar_order": 4
      },
      {
        "t": "2020-01-01T00:00:58Z",
        "r_squared": 0.0057,
        "critical_value": 0.7683,
        "ar_order": 4
      },
      {
        "t": "2020-01-01T00:00:59Z",
        "r_squared": 0.1449,
        "critical_value": 0.6402,
        "ar_order": 3
      },
      {
        "t": "2020-01-01T00:01:00Z",
        "r_squared": 0.002586,
        "critical_value": 0.7683,
        "ar_order": 4
      },
      {
        "t": "2020-01-01T00:01:01Z",
        "r_squared": 0.1632,
        "critical_value": 0.7683,
        "ar_order": 4
      },
      {
        "t": "2020-01-01T00:01:02Z",
        "r_squared": 0.004873,
        "critical_value": 0.4802,
        "ar_order": 1
      },
      {
        "t": "2020-01-01T00:01:03Z",
        "r_squared": 0.04022,
        "critical_value": 0.5488,
        "ar_order": 2
      },
      {
        "t": "2020-01-01T00:01:04Z",
        "r_squared": 0.03178,
        "critical_value": 0.7683,
        "ar_order": 4
      },
      {
        "t": "2020-01-01T00:01:05Z",
        "r_squared": 0.03095,
        "critical_value": 0.7683,
        "ar_order": 4
      },
      {
        "t": "2020-01-01T00:01:06Z",
        "r_squared": 0.1076,
        "critical_value": 0.7683,
        "ar_order": 4
      },
      {
        "t": "2020-01-01T00:01:07Z",
        "r_squared": 0.2181,
        "critical_value": 0.7683,
        "ar_order": 4
      },
      {
        "t": "2020-01-01T00:01:08Z",
        "r_squared": 0.4224,
        "critical_value": 0.7683,
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      },
      {
        "t": "2020-01-01T00:01:09Z",
        "r_squared": 0.2109,
        "critical_value": 0.7683,
        "ar_order": 4
      },
      {
        "t": "2020-01-01T00:01:10Z",
        "r_squared": 0.05782,
        "critical_value": 0.6402,
        "ar_order": 3
      },
      {
        "t": "2020-01-01T00:01:11Z",
        "r_squared": 0.2873,
        "critical_value": 0.7683,
        "ar_order": 4
      },
      {
        "t": "2020-01-01T00:01:12Z",
        "r_squared": 0.2194,
        "critical_value": 0.7683,
        "ar_order": 4
      },
      {
        "t": "2020-01-01T00:01:13Z",
        "r_squared": 0.0004768,
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      },
      {
        "t": "2020-01-01T00:01:14Z",
        "r_squared": 0.0003442,
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      },
      {
        "t": "2020-01-01T00:01:15Z",
        "r_squared": 0.1037,
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      },
      {
        "t": "2020-01-01T00:01:16Z",
        "r_squared": 0.0006259,
        "critical_value": 0.7683,
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      },
      {
        "t": "2020-01-01T00:01:17Z",
        "r_squared": 0.6853,
        "critical_value": 0.7683,
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      },
      {
        "t": "2020-01-01T00:01:18Z",
        "r_squared": 0.009238,
        "critical_value": 0.7683,
        "ar_order": 4
      },
      {
        "t": "2020-01-01T00:01:19Z",
        "r_squared": 0.02107,
        "critical_value": 0.7683,
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      },
      {
        "t": "2020-01-01T00:01:20Z",
        "r_squared": 0.06531,
        "critical_value": 0.5488,
        "ar_order": 2
      },
      {
        "t": "2020-01-01T00:01:21Z",
        "r_squared": 0.006273,
        "critical_value": 0.7683,
        "ar_order": 4
      },
      {
        "t": "2020-01-01T00:01:22Z",
        "r_squared": 0.04184,
        "critical_value": 0.7683,
        "ar_order": 4
      },
      {
        "t": "2020-01-01T00:01:23Z",
        "r_squared": 0.1358,
        "critical_value": 0.7683,
        "ar_order": 4
      },
      {
        "t": "2020-01-01T00:01:24Z",
        "r_squared": 0.002292,
        "critical_value": 0.7683,
        "ar_order": 4
      },
      {
        "t": "2020-01-01T00:01:25Z",
        "r_squared": 0.03404,
        "critical_value": 0.7683,
        "ar_order": 4
      },
      {
        "t": "2020-01-01T00:01:26Z",
        "r_squared": 0.04066,
        "critical_value": 0.7683,
        "ar_order": 4
      },
      {
        "t": "2020-01-01T00:01:27Z",
        "r_squared": 0.004074,
        "critical_value": 0.7683,
        "ar_order": 4
      },
      {
        "t": "2020-01-01T00:01:28Z",
        "r_squared": 0.04182,
        "critical_value": 0.7683,
        "ar_order": 4
      },
      {
        "t": "2020-01-01T00:01:29Z",
        "r_squared": 0.1797,
        "critical_value": 0.7683,
        "ar_order": 4
      },
      {
        "t": "2020-01-01T00:01:30Z",
        "r_squared": 0.0224,
        "critical_value": 0.7683,
        "ar_order": 4
      },
      {
        "t": "2020-01-01T00:01:31Z",
        "r_squared": 0.04292,
        "critical_value": 0.7683,
        "ar_order": 4
      },
      {
        "t": "2020-01-01T00:01:32Z",
        "r_squared": 0.07431,
        "critical_value": 0.5488,
        "ar_order": 2
      },
      {
        "t": "2020-01-01T00:01:33Z",
        "r_squared": 0.1252,
        "critical_value": 0.4802,
        "ar_order": 1
      },
      {
        "t": "2020-01-01T00:01:34Z",
        "r_squared": 0.02185,
        "critical_value": 0.7683,
        "ar_order": 4
      },
      {
        "t": "2020-01-01T00:01:35Z",
        "r_squared": 0.003631,
        "critical_value": 0.7683,
        "ar_order": 4
      },
      {
        "t": "2020-01-01T00:01:36Z",
        "r_squared": 0.01591,
        "critical_value": 0.7683,
        "ar_order": 4
      },
      {
        "t": "2020-01-01T00:01:37Z",
        "r_squared": 0.04491,
        "critical_value": 0.7683,
        "ar_order": 4
      },
      {
        "t": "2020-01-01T00:01:38Z",
        "r_squared": 0.06367,
        "critical_value": 0.4802,
        "ar_order": 1
      },
      {
        "t": "2020-01-01T00:01:39Z",
        "r_squared": 0.2203,
        "critical_value": 0.7683,
        "ar_order": 4
      }
    ]
  }
}
        

drift diffusion jump

POST /invocation/drift-diffusion-jump

Early warning signal detection
univariate | nonparametric

The nonparametric Drift-Diffusion-Jump model models a wide variety of unknown underlying time series data generating processes and estimates drift, diffusion and jump metrics over data and time. These metrics can capture the dynamical phenomena of rising memory, rising variability, and flickering. The drift metric quantifies the instantaneous local rate of change in the time series. The diffusion metric quantifies the standard deviation of relatively small shocks at each time step. The jump metric quantifies relatively large intermittent shocks. Total variance combines diffusion and jumps. Conditional variance signifies variance with a positive relationship with variance at previous time steps and rises to infinity at a critical transition.

ARGUMENTS

time_series
REQUIREDarray(length: 1)

An array of objects, each representing 1 distinct time series.

reproduction
optionalbooleandefault: false

Return imputed values, applied data transformations and arguments. Useful for reproduction of the results.

precision
optionalobject

Decimal point precision of the output data.

kernel_bandwidth_factor
optionalnumberdefault: 0.6min: 0.1max: 1

Is multiplied with the standard deviation of the complete time series to give the Gaussian kernel bandwidth.

kernel_points
optionalintegerdefault: 500min: 250max: 1000

Number of points used for the kernel. Use caution when selecting values above the default value.

RETURNS

// Tokenization skipped
{
  "kernel_bandwidth_factor": 0.6,
  "kernel_points": 500,
  "reproduction": false,
  "precision": {
    "digits": 4,
    "method": "significant"
  },
  "time_series": [
    {
      "data": {
        "2020-01-01T00:00:00Z": 28.0137,
        "2020-01-01T00:00:01Z": 27.8591,
        "2020-01-01T00:00:02Z": 27.6281,
        "2020-01-01T00:00:03Z": 27.0703,
        "2020-01-01T00:00:04Z": 25.7454,
        "2020-01-01T00:00:05Z": 27.0635,
        "2020-01-01T00:00:06Z": 27.9731,
        "2020-01-01T00:00:07Z": 28.1618,
        "2020-01-01T00:00:08Z": 29.5978,
        "2020-01-01T00:00:09Z": 30.9978,
        "2020-01-01T00:00:10Z": 31.0237,
        "2020-01-01T00:00:11Z": 31.6535,
        "2020-01-01T00:00:12Z": 32.0346,
        "2020-01-01T00:00:13Z": 31.8492,
        "2020-01-01T00:00:14Z": 32.3419,
        "2020-01-01T00:00:15Z": 32.0351,
        "2020-01-01T00:00:16Z": 30.7687,
        "2020-01-01T00:00:17Z": 30.374,
        "2020-01-01T00:00:18Z": 28.1942,
        "2020-01-01T00:00:19Z": 25.9453,
        "2020-01-01T00:00:20Z": 23.6843,
        "2020-01-01T00:00:21Z": 21.943,
        "2020-01-01T00:00:22Z": 20.309,
        "2020-01-01T00:00:23Z": 19.3427,
        "2020-01-01T00:00:24Z": 19.3478,
        "2020-01-01T00:00:25Z": 19.7972,
        "2020-01-01T00:00:26Z": 21.2299,
        "2020-01-01T00:00:27Z": 22.4813,
        "2020-01-01T00:00:28Z": 23.2128,
        "2020-01-01T00:00:29Z": 22.7081,
        "2020-01-01T00:00:30Z": 23.1786,
        "2020-01-01T00:00:31Z": 22.805,
        "2020-01-01T00:00:32Z": 23.4281,
        "2020-01-01T00:00:33Z": 24.5025,
        "2020-01-01T00:00:34Z": 24.213,
        "2020-01-01T00:00:35Z": 23.3072,
        "2020-01-01T00:00:36Z": 23.7229,
        "2020-01-01T00:00:37Z": 23.1353,
        "2020-01-01T00:00:38Z": 24.0197,
        "2020-01-01T00:00:39Z": 23.3354,
        "2020-01-01T00:00:40Z": 24.171,
        "2020-01-01T00:00:41Z": 23.8188,
        "2020-01-01T00:00:42Z": 24.6172,
        "2020-01-01T00:00:43Z": 24.2777,
        "2020-01-01T00:00:44Z": 24.2283,
        "2020-01-01T00:00:45Z": 25.1955,
        "2020-01-01T00:00:46Z": 26.4958,
        "2020-01-01T00:00:47Z": 28.3069,
        "2020-01-01T00:00:48Z": 29.7687,
        "2020-01-01T00:00:49Z": 30.9865,
        "2020-01-01T00:00:50Z": 29.7695,
        "2020-01-01T00:00:51Z": 30.1204,
        "2020-01-01T00:00:52Z": 31.742,
        "2020-01-01T00:00:53Z": 34.6089,
        "2020-01-01T00:00:54Z": 36.054,
        "2020-01-01T00:00:55Z": 36.3756,
        "2020-01-01T00:00:56Z": 37.36,
        "2020-01-01T00:00:57Z": 38.1193,
        "2020-01-01T00:00:58Z": 38.5563,
        "2020-01-01T00:00:59Z": 40.6662,
        "2020-01-01T00:01:00Z": 42.6862,
        "2020-01-01T00:01:01Z": 45.0665,
        "2020-01-01T00:01:02Z": 46.3616,
        "2020-01-01T00:01:03Z": 46.8506,
        "2020-01-01T00:01:04Z": 47.7675,
        "2020-01-01T00:01:05Z": 47.6054,
        "2020-01-01T00:01:06Z": 46.2565,
        "2020-01-01T00:01:07Z": 45.536,
        "2020-01-01T00:01:08Z": 46.3415,
        "2020-01-01T00:01:09Z": 48.0423,
        "2020-01-01T00:01:10Z": 50.8812,
        "2020-01-01T00:01:11Z": 52.6965,
        "2020-01-01T00:01:12Z": 54.7823,
        "2020-01-01T00:01:13Z": 53.512,
        "2020-01-01T00:01:14Z": 53.2565,
        "2020-01-01T00:01:15Z": 53.0911,
        "2020-01-01T00:01:16Z": 52.4152,
        "2020-01-01T00:01:17Z": 51.8234,
        "2020-01-01T00:01:18Z": 50.2512,
        "2020-01-01T00:01:19Z": 51.0036,
        "2020-01-01T00:01:20Z": 51.9257,
        "2020-01-01T00:01:21Z": 52.5759,
        "2020-01-01T00:01:22Z": 54.1171,
        "2020-01-01T00:01:23Z": 55.4398,
        "2020-01-01T00:01:24Z": 55.5233,
        "2020-01-01T00:01:25Z": 53.8893,
        "2020-01-01T00:01:26Z": 52.8306,
        "2020-01-01T00:01:27Z": 52.2715,
        "2020-01-01T00:01:28Z": 51.0688,
        "2020-01-01T00:01:29Z": 51.6046,
        "2020-01-01T00:01:30Z": 51.6625,
        "2020-01-01T00:01:31Z": 51.1545,
        "2020-01-01T00:01:32Z": 50.4331,
        "2020-01-01T00:01:33Z": 49.8225,
        "2020-01-01T00:01:34Z": 47.5345,
        "2020-01-01T00:01:35Z": 48.5842,
        "2020-01-01T00:01:36Z": 49.3886,
        "2020-01-01T00:01:37Z": 50.4767,
        "2020-01-01T00:01:38Z": 49.5141,
        "2020-01-01T00:01:39Z": 50.3534
      },
      "imputation": {
        "method": "linear",
        "ma_window_size": 10
      },
      "transformations": {
        "box_cox": {
          "apply": false,
          "lambda": "auto",
          "method": "guerrero",
          "upper": 2,
          "lower": -1
        },
        "log": {
          "apply": false,
          "base": "e",
          "factor": null,
          "constant": 1
        },
        "seasonal_diff": {
          "apply": false,
          "period": "auto",
          "n_diffs": "auto",
          "test": "ss",
          "alpha": 0.05
        },
        "first_diff": {
          "apply": false,
          "n_diffs": "auto",
          "test": "kpss",
          "type": "level",
          "alpha": 0.05
        }
      }
    }
  ]
}
{
  "report": {
    "computation_time": 426.35
  },
  "result": {
    "reproduction": {},
    "data": {
      "time": [
        {
          "t": "2020-01-01T00:00:00Z",
          "drift": 0.1893,
          "diffusion": 0,
          "jump": 1.419,
          "total_variance": 1.311,
          "conditional_variance": 25.69
        },
        {
          "t": "2020-01-01T00:00:01Z",
          "drift": 0.1869,
          "diffusion": 0,
          "jump": 1.41,
          "total_variance": 1.307,
          "conditional_variance": 25.28
        },
        {
          "t": "2020-01-01T00:00:02Z",
          "drift": 0.1835,
          "diffusion": 0,
          "jump": 1.397,
          "total_variance": 1.301,
          "conditional_variance": 24.7
        },
        {
          "t": "2020-01-01T00:00:03Z",
          "drift": 0.1759,
          "diffusion": 0,
          "jump": 1.364,
          "total_variance": 1.286,
          "conditional_variance": 23.4
        },
        {
          "t": "2020-01-01T00:00:04Z",
          "drift": 0.1607,
          "diffusion": 0,
          "jump": 1.29,
          "total_variance": 1.253,
          "conditional_variance": 20.8
        },
        {
          "t": "2020-01-01T00:00:05Z",
          "drift": 0.1758,
          "diffusion": 0,
          "jump": 1.364,
          "total_variance": 1.286,
          "conditional_variance": 23.38
        },
        {
          "t": "2020-01-01T00:00:06Z",
          "drift": 0.1886,
          "diffusion": 0,
          "jump": 1.417,
          "total_variance": 1.31,
          "conditional_variance": 25.58
        },
        {
          "t": "2020-01-01T00:00:07Z",
          "drift": 0.1916,
          "diffusion": 0,
          "jump": 1.428,
          "total_variance": 1.315,
          "conditional_variance": 26.09
        },
        {
          "t": "2020-01-01T00:00:08Z",
          "drift": 0.2172,
          "diffusion": 0,
          "jump": 1.516,
          "total_variance": 1.354,
          "conditional_variance": 30.66
        },
        {
          "t": "2020-01-01T00:00:09Z",
          "drift": 0.2482,
          "diffusion": 0,
          "jump": 1.605,
          "total_variance": 1.394,
          "conditional_variance": 36.63
        },
        {
          "t": "2020-01-01T00:00:10Z",
          "drift": 0.2488,
          "diffusion": 0,
          "jump": 1.607,
          "total_variance": 1.395,
          "conditional_variance": 36.75
        },
        {
          "t": "2020-01-01T00:00:11Z",
          "drift": 0.2649,
          "diffusion": 0,
          "jump": 1.648,
          "total_variance": 1.414,
          "conditional_variance": 40.04
        },
        {
          "t": "2020-01-01T00:00:12Z",
          "drift": 0.2752,
          "diffusion": 0,
          "jump": 1.673,
          "total_variance": 1.425,
          "conditional_variance": 42.22
        },
        {
          "t": "2020-01-01T00:00:13Z",
          "drift": 0.2701,
          "diffusion": 0,
          "jump": 1.661,
          "total_variance": 1.42,
          "conditional_variance": 41.14
        },
        {
          "t": "2020-01-01T00:00:14Z",
          "drift": 0.2838,
          "diffusion": 0,
          "jump": 1.694,
          "total_variance": 1.435,
          "conditional_variance": 44.09
        },
        {
          "t": "2020-01-01T00:00:15Z",
          "drift": 0.2752,
          "diffusion": 0,
          "jump": 1.673,
          "total_variance": 1.425,
          "conditional_variance": 42.22
        },
        {
          "t": "2020-01-01T00:00:16Z",
          "drift": 0.2427,
          "diffusion": 0,
          "jump": 1.59,
          "total_variance": 1.387,
          "conditional_variance": 35.53
        },
        {
          "t": "2020-01-01T00:00:17Z",
          "drift": 0.2336,
          "diffusion": 0,
          "jump": 1.565,
          "total_variance": 1.376,
          "conditional_variance": 33.76
        },
        {
          "t": "2020-01-01T00:00:18Z",
          "drift": 0.1921,
          "diffusion": 0,
          "jump": 1.43,
          "total_variance": 1.316,
          "conditional_variance": 26.18
        },
        {
          "t": "2020-01-01T00:00:19Z",
          "drift": 0.1627,
          "diffusion": 0,
          "jump": 1.301,
          "total_variance": 1.258,
          "conditional_variance": 21.15
        },
        {
          "t": "2020-01-01T00:00:20Z",
          "drift": 0.144,
          "diffusion": 0.0002276,
          "jump": 1.18,
          "total_variance": 1.205,
          "conditional_variance": 17.74
        },
        {
          "t": "2020-01-01T00:00:21Z",
          "drift": 0.1351,
          "diffusion": 0.0483,
          "jump": 1.095,
          "total_variance": 1.166,
          "conditional_variance": 15.76
        },
        {
          "t": "2020-01-01T00:00:22Z",
          "drift": 0.1303,
          "diffusion": 0.0895,
          "jump": 1.021,
          "total_variance": 1.132,
          "conditional_variance": 14.23
        },
        {
          "t": "2020-01-01T00:00:23Z",
          "drift": 0.1287,
          "diffusion": 0.112,
          "jump": 0.9803,
          "total_variance": 1.112,
          "conditional_variance": 13.43
        },
        {
          "t": "2020-01-01T00:00:24Z",
          "drift": 0.1287,
          "diffusion": 0.1119,
          "jump": 0.9805,
          "total_variance": 1.113,
          "conditional_variance": 13.43
        },
        {
          "t": "2020-01-01T00:00:25Z",
          "drift": 0.1293,
          "diffusion": 0.1016,
          "jump": 0.9992,
          "total_variance": 1.121,
          "conditional_variance": 13.8
        },
        {
          "t": "2020-01-01T00:00:26Z",
          "drift": 0.1326,
          "diffusion": 0.06677,
          "jump": 1.062,
          "total_variance": 1.151,
          "conditional_variance": 15.06
        },
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          "conditional_variance": 25.19
        },
        {
          "x": 48.42,
          "drift": 0.2838,
          "diffusion": 0,
          "jump": 1.772,
          "total_variance": 1.522,
          "conditional_variance": 24.84
        },
        {
          "x": 48.49,
          "drift": 0.2813,
          "diffusion": 0,
          "jump": 1.768,
          "total_variance": 1.52,
          "conditional_variance": 24.49
        },
        {
          "x": 48.56,
          "drift": 0.2788,
          "diffusion": 0,
          "jump": 1.764,
          "total_variance": 1.518,
          "conditional_variance": 24.15
        },
        {
          "x": 48.64,
          "drift": 0.2763,
          "diffusion": 0,
          "jump": 1.76,
          "total_variance": 1.517,
          "conditional_variance": 23.82
        },
        {
          "x": 48.71,
          "drift": 0.2738,
          "diffusion": 0,
          "jump": 1.756,
          "total_variance": 1.515,
          "conditional_variance": 23.49
        },
        {
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          "diffusion": 0,
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          "conditional_variance": 23.17
        },
        {
          "x": 48.85,
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          "diffusion": 0,
          "jump": 1.748,
          "total_variance": 1.511,
          "conditional_variance": 22.85
        },
        {
          "x": 48.93,
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          "diffusion": 0,
          "jump": 1.744,
          "total_variance": 1.51,
          "conditional_variance": 22.54
        },
        {
          "x": 49,
          "drift": 0.264,
          "diffusion": 0,
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          "total_variance": 1.508,
          "conditional_variance": 22.23
        },
        {
          "x": 49.07,
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          "conditional_variance": 21.93
        },
        {
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          "conditional_variance": 21.63
        },
        {
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          "conditional_variance": 21.34
        },
        {
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          "total_variance": 1.501,
          "conditional_variance": 21.05
        },
        {
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          "conditional_variance": 20.77
        },
        {
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          "conditional_variance": 20.5
        },
        {
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          "conditional_variance": 20.22
        },
        {
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          "conditional_variance": 19.96
        },
        {
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          "diffusion": 0,
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          "conditional_variance": 19.7
        },
        {
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          "conditional_variance": 19.44
        },
        {
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        },
        {
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        },
        {
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          "conditional_variance": 18.69
        },
        {
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          "conditional_variance": 18.46
        },
        {
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          "conditional_variance": 18.22
        },
        {
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          "conditional_variance": 17.99
        },
        {
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          "diffusion": 0,
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          "conditional_variance": 17.76
        },
        {
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          "diffusion": 0,
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          "conditional_variance": 17.54
        },
        {
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          "diffusion": 0,
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          "conditional_variance": 17.32
        },
        {
          "x": 50.45,
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          "diffusion": 0,
          "jump": 1.664,
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          "conditional_variance": 17.11
        },
        {
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          "diffusion": 0,
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          "conditional_variance": 16.9
        },
        {
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          "diffusion": 0,
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          "conditional_variance": 16.69
        },
        {
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          "diffusion": 0,
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          "total_variance": 1.469,
          "conditional_variance": 16.49
        },
        {
          "x": 50.74,
          "drift": 0.2075,
          "diffusion": 0,
          "jump": 1.649,
          "total_variance": 1.467,
          "conditional_variance": 16.29
        },
        {
          "x": 50.81,
          "drift": 0.2053,
          "diffusion": 0,
          "jump": 1.645,
          "total_variance": 1.466,
          "conditional_variance": 16.09
        },
        {
          "x": 50.88,
          "drift": 0.203,
          "diffusion": 0,
          "jump": 1.642,
          "total_variance": 1.464,
          "conditional_variance": 15.9
        },
        {
          "x": 50.96,
          "drift": 0.2008,
          "diffusion": 0,
          "jump": 1.638,
          "total_variance": 1.463,
          "conditional_variance": 15.71
        },
        {
          "x": 51.03,
          "drift": 0.1986,
          "diffusion": 0,
          "jump": 1.634,
          "total_variance": 1.461,
          "conditional_variance": 15.53
        },
        {
          "x": 51.1,
          "drift": 0.1964,
          "diffusion": 0,
          "jump": 1.631,
          "total_variance": 1.459,
          "conditional_variance": 15.35
        },
        {
          "x": 51.17,
          "drift": 0.1942,
          "diffusion": 0,
          "jump": 1.627,
          "total_variance": 1.458,
          "conditional_variance": 15.17
        },
        {
          "x": 51.25,
          "drift": 0.192,
          "diffusion": 0,
          "jump": 1.624,
          "total_variance": 1.456,
          "conditional_variance": 14.99
        },
        {
          "x": 51.32,
          "drift": 0.1898,
          "diffusion": 0,
          "jump": 1.62,
          "total_variance": 1.455,
          "conditional_variance": 14.82
        },
        {
          "x": 51.39,
          "drift": 0.1877,
          "diffusion": 0,
          "jump": 1.617,
          "total_variance": 1.453,
          "conditional_variance": 14.65
        },
        {
          "x": 51.46,
          "drift": 0.1855,
          "diffusion": 0,
          "jump": 1.613,
          "total_variance": 1.452,
          "conditional_variance": 14.49
        },
        {
          "x": 51.54,
          "drift": 0.1833,
          "diffusion": 0,
          "jump": 1.61,
          "total_variance": 1.45,
          "conditional_variance": 14.32
        },
        {
          "x": 51.61,
          "drift": 0.1812,
          "diffusion": 0,
          "jump": 1.606,
          "total_variance": 1.449,
          "conditional_variance": 14.16
        },
        {
          "x": 51.68,
          "drift": 0.1791,
          "diffusion": 0,
          "jump": 1.603,
          "total_variance": 1.447,
          "conditional_variance": 14.01
        },
        {
          "x": 51.75,
          "drift": 0.1769,
          "diffusion": 0,
          "jump": 1.599,
          "total_variance": 1.446,
          "conditional_variance": 13.85
        },
        {
          "x": 51.83,
          "drift": 0.1748,
          "diffusion": 0,
          "jump": 1.596,
          "total_variance": 1.444,
          "conditional_variance": 13.7
        },
        {
          "x": 51.9,
          "drift": 0.1727,
          "diffusion": 0,
          "jump": 1.592,
          "total_variance": 1.443,
          "conditional_variance": 13.55
        },
        {
          "x": 51.97,
          "drift": 0.1706,
          "diffusion": 0,
          "jump": 1.589,
          "total_variance": 1.441,
          "conditional_variance": 13.41
        },
        {
          "x": 52.04,
          "drift": 0.1685,
          "diffusion": 0,
          "jump": 1.585,
          "total_variance": 1.44,
          "conditional_variance": 13.27
        },
        {
          "x": 52.12,
          "drift": 0.1664,
          "diffusion": 0,
          "jump": 1.582,
          "total_variance": 1.438,
          "conditional_variance": 13.13
        },
        {
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          "drift": 0.1644,
          "diffusion": 0,
          "jump": 1.579,
          "total_variance": 1.437,
          "conditional_variance": 12.99
        },
        {
          "x": 52.26,
          "drift": 0.1623,
          "diffusion": 0,
          "jump": 1.575,
          "total_variance": 1.435,
          "conditional_variance": 12.85
        },
        {
          "x": 52.33,
          "drift": 0.1603,
          "diffusion": 0,
          "jump": 1.572,
          "total_variance": 1.434,
          "conditional_variance": 12.72
        },
        {
          "x": 52.41,
          "drift": 0.1582,
          "diffusion": 0,
          "jump": 1.569,
          "total_variance": 1.432,
          "conditional_variance": 12.59
        },
        {
          "x": 52.48,
          "drift": 0.1562,
          "diffusion": 0,
          "jump": 1.565,
          "total_variance": 1.431,
          "conditional_variance": 12.46
        },
        {
          "x": 52.55,
          "drift": 0.1541,
          "diffusion": 0,
          "jump": 1.562,
          "total_variance": 1.43,
          "conditional_variance": 12.34
        },
        {
          "x": 52.62,
          "drift": 0.1521,
          "diffusion": 0,
          "jump": 1.559,
          "total_variance": 1.428,
          "conditional_variance": 12.22
        },
        {
          "x": 52.7,
          "drift": 0.1501,
          "diffusion": 0,
          "jump": 1.555,
          "total_variance": 1.427,
          "conditional_variance": 12.09
        },
        {
          "x": 52.77,
          "drift": 0.1481,
          "diffusion": 0,
          "jump": 1.552,
          "total_variance": 1.425,
          "conditional_variance": 11.98
        },
        {
          "x": 52.84,
          "drift": 0.1461,
          "diffusion": 0,
          "jump": 1.549,
          "total_variance": 1.424,
          "conditional_variance": 11.86
        },
        {
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          "drift": 0.1441,
          "diffusion": 0,
          "jump": 1.546,
          "total_variance": 1.423,
          "conditional_variance": 11.75
        },
        {
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          "drift": 0.1422,
          "diffusion": 0,
          "jump": 1.542,
          "total_variance": 1.421,
          "conditional_variance": 11.63
        },
        {
          "x": 53.06,
          "drift": 0.1402,
          "diffusion": 0,
          "jump": 1.539,
          "total_variance": 1.42,
          "conditional_variance": 11.52
        },
        {
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          "drift": 0.1382,
          "diffusion": 0,
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          "conditional_variance": 11.41
        },
        {
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          "diffusion": 0,
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          "conditional_variance": 11.31
        },
        {
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          "conditional_variance": 11.2
        },
        {
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          "diffusion": 0,
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        },
        {
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        },
        {
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        },
        {
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          "diffusion": 0,
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        },
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        },
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        },
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        },
        {
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          "diffusion": 0,
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          "conditional_variance": 10.17
        },
        {
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          "drift": 0.1117,
          "diffusion": 0,
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          "conditional_variance": 10.09
        },
        {
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          "drift": 0.1098,
          "diffusion": 0,
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          "conditional_variance": 10
        },
        {
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          "diffusion": 0,
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          "conditional_variance": 9.922
        },
        {
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          "diffusion": 0,
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          "conditional_variance": 9.842
        },
        {
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          "conditional_variance": 9.763
        },
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        },
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          "diffusion": 0,
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          "conditional_variance": 9.61
        },
        {
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          "diffusion": 0,
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          "total_variance": 1.392,
          "conditional_variance": 9.535
        },
        {
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          "diffusion": 0,
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          "conditional_variance": 9.462
        },
        {
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          "diffusion": 0,
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          "conditional_variance": 9.39
        },
        {
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          "diffusion": 0,
          "jump": 1.463,
          "total_variance": 1.388,
          "conditional_variance": 9.319
        },
        {
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          "drift": 0.09189,
          "diffusion": 0,
          "jump": 1.46,
          "total_variance": 1.387,
          "conditional_variance": 9.249
        },
        {
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          "drift": 0.09013,
          "diffusion": 0,
          "jump": 1.457,
          "total_variance": 1.386,
          "conditional_variance": 9.181
        },
        {
          "x": 55.09,
          "drift": 0.08839,
          "diffusion": 0,
          "jump": 1.454,
          "total_variance": 1.385,
          "conditional_variance": 9.113
        },
        {
          "x": 55.16,
          "drift": 0.08665,
          "diffusion": 0,
          "jump": 1.451,
          "total_variance": 1.384,
          "conditional_variance": 9.047
        },
        {
          "x": 55.23,
          "drift": 0.08492,
          "diffusion": 0,
          "jump": 1.449,
          "total_variance": 1.383,
          "conditional_variance": 8.982
        },
        {
          "x": 55.31,
          "drift": 0.08319,
          "diffusion": 0,
          "jump": 1.446,
          "total_variance": 1.382,
          "conditional_variance": 8.918
        },
        {
          "x": 55.38,
          "drift": 0.08147,
          "diffusion": 0,
          "jump": 1.443,
          "total_variance": 1.38,
          "conditional_variance": 8.855
        },
        {
          "x": 55.45,
          "drift": 0.07976,
          "diffusion": 0,
          "jump": 1.44,
          "total_variance": 1.379,
          "conditional_variance": 8.793
        },
        {
          "x": 55.52,
          "drift": 0.07806,
          "diffusion": 0,
          "jump": 1.437,
          "total_variance": 1.378,
          "conditional_variance": 8.732
        }
      ]
    }
  }
}
        

early warning signals

POST /invocation/early-warning-signals

Early warning signal detection
univariate | parametric | fast data

Estimates various statistical moments within a moving window along the time series. These estimates serve as potential early warning signals for critical transitions and are differently associated with the dynamical phenomena of rising memory, rising variability, and flickering.

ARGUMENTS

time_series
REQUIREDarray(length: 1)

An array of objects, each representing 1 distinct time series.

reproduction
optionalbooleandefault: false

Return imputed values, applied data transformations and arguments. Useful for reproduction of the results.

precision
optionalobject

Decimal point precision of the output data.

method
optionalstringdefault: acf1
valid values: acf1, ar1, kurtosis, return_rate, sd, skewness, spectral_ratio

The statistical moment to be estimated. acf1 is the autocorrelation at lag 1. ar1 is the autoregressive coefficient of an AR(1) model. return_rate (to equilibrium) is the inverse of the AR(1) coefficient. sd is the standard deviation. spectral_ratio is the ratio of the spectral density at low (0.05) to high frequency (0.5).

acf1, ar1, return_rate and spectral_ratio are associated with the dynamical phenomenon of rising memory; skewness, kurtosis and sd with rising variability and flickering.

window_size
optionalintegerdefault: 10min: 10

The size of the moving window in number of data points. Changed to window_size = floor(n/2), if window_size > n/2.

RETURNS

{
  "method": "acf1",
  "window_size": 10,
  "reproduction": false,
  "precision": {
    "digits": 4,
    "method": "significant"
  },
  "time_series": [
    {
      "data": {
        "2020-01-01T00:00:00Z": 28.0137,
        "2020-01-01T00:00:01Z": 27.8591,
        "2020-01-01T00:00:02Z": 27.6281,
        "2020-01-01T00:00:03Z": 27.0703,
        "2020-01-01T00:00:04Z": 25.7454,
        "2020-01-01T00:00:05Z": 27.0635,
        "2020-01-01T00:00:06Z": 27.9731,
        "2020-01-01T00:00:07Z": 28.1618,
        "2020-01-01T00:00:08Z": 29.5978,
        "2020-01-01T00:00:09Z": 30.9978,
        "2020-01-01T00:00:10Z": 31.0237,
        "2020-01-01T00:00:11Z": 31.6535,
        "2020-01-01T00:00:12Z": 32.0346,
        "2020-01-01T00:00:13Z": 31.8492,
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      {
        "t": "2020-01-01T00:00:48Z",
        "acf1": 0.2391
      },
      {
        "t": "2020-01-01T00:00:49Z",
        "acf1": 0.4371
      },
      {
        "t": "2020-01-01T00:00:50Z",
        "acf1": 0.1884
      },
      {
        "t": "2020-01-01T00:00:51Z",
        "acf1": 0.2761
      },
      {
        "t": "2020-01-01T00:00:52Z",
        "acf1": 0.2271
      },
      {
        "t": "2020-01-01T00:00:53Z",
        "acf1": 0.2186
      },
      {
        "t": "2020-01-01T00:00:54Z",
        "acf1": 0.2937
      },
      {
        "t": "2020-01-01T00:00:55Z",
        "acf1": 0.2574
      },
      {
        "t": "2020-01-01T00:00:56Z",
        "acf1": 0.2534
      },
      {
        "t": "2020-01-01T00:00:57Z",
        "acf1": 0.2307
      },
      {
        "t": "2020-01-01T00:00:58Z",
        "acf1": 0.224
      },
      {
        "t": "2020-01-01T00:00:59Z",
        "acf1": 0.1984
      },
      {
        "t": "2020-01-01T00:01:00Z",
        "acf1": 0.1653
      },
      {
        "t": "2020-01-01T00:01:01Z",
        "acf1": 0.3094
      },
      {
        "t": "2020-01-01T00:01:02Z",
        "acf1": 0.2485
      },
      {
        "t": "2020-01-01T00:01:03Z",
        "acf1": 0.2871
      },
      {
        "t": "2020-01-01T00:01:04Z",
        "acf1": 0.3765
      },
      {
        "t": "2020-01-01T00:01:05Z",
        "acf1": 0.3502
      },
      {
        "t": "2020-01-01T00:01:06Z",
        "acf1": 0.4572
      },
      {
        "t": "2020-01-01T00:01:07Z",
        "acf1": 0.6379
      },
      {
        "t": "2020-01-01T00:01:08Z",
        "acf1": 0.6686
      },
      {
        "t": "2020-01-01T00:01:09Z",
        "acf1": 0.5832
      },
      {
        "t": "2020-01-01T00:01:10Z",
        "acf1": 0.4922
      },
      {
        "t": "2020-01-01T00:01:11Z",
        "acf1": 0.6244
      },
      {
        "t": "2020-01-01T00:01:12Z",
        "acf1": 0.6677
      },
      {
        "t": "2020-01-01T00:01:13Z",
        "acf1": 0.3991
      },
      {
        "t": "2020-01-01T00:01:14Z",
        "acf1": 0.4872
      },
      {
        "t": "2020-01-01T00:01:15Z",
        "acf1": 0.449
      },
      {
        "t": "2020-01-01T00:01:16Z",
        "acf1": 0.4055
      },
      {
        "t": "2020-01-01T00:01:17Z",
        "acf1": 0.514
      },
      {
        "t": "2020-01-01T00:01:18Z",
        "acf1": 0.5122
      },
      {
        "t": "2020-01-01T00:01:19Z",
        "acf1": 0.3442
      },
      {
        "t": "2020-01-01T00:01:20Z",
        "acf1": 0.1882
      },
      {
        "t": "2020-01-01T00:01:21Z",
        "acf1": -0.06844
      },
      {
        "t": "2020-01-01T00:01:22Z",
        "acf1": 0.3118
      },
      {
        "t": "2020-01-01T00:01:23Z",
        "acf1": 0.4945
      },
      {
        "t": "2020-01-01T00:01:24Z",
        "acf1": 0.4701
      },
      {
        "t": "2020-01-01T00:01:25Z",
        "acf1": 0.3543
      },
      {
        "t": "2020-01-01T00:01:26Z",
        "acf1": 0.4534
      },
      {
        "t": "2020-01-01T00:01:27Z",
        "acf1": 0.4255
      },
      {
        "t": "2020-01-01T00:01:28Z",
        "acf1": 0.6279
      },
      {
        "t": "2020-01-01T00:01:29Z",
        "acf1": 0.5365
      },
      {
        "t": "2020-01-01T00:01:30Z",
        "acf1": 0.5169
      },
      {
        "t": "2020-01-01T00:01:31Z",
        "acf1": 0.3984
      },
      {
        "t": "2020-01-01T00:01:32Z",
        "acf1": 0.1393
      },
      {
        "t": "2020-01-01T00:01:33Z",
        "acf1": -0.03978
      },
      {
        "t": "2020-01-01T00:01:34Z",
        "acf1": 0.1144
      },
      {
        "t": "2020-01-01T00:01:35Z",
        "acf1": -0.34
      },
      {
        "t": "2020-01-01T00:01:36Z",
        "acf1": -0.07904
      },
      {
        "t": "2020-01-01T00:01:37Z",
        "acf1": 0.05081
      },
      {
        "t": "2020-01-01T00:01:38Z",
        "acf1": 0.02687
      },
      {
        "t": "2020-01-01T00:01:39Z",
        "acf1": -0.05995
      }
    ]
  }
}
        

granger causality

POST /invocation/granger-causality

Causality inference
multivariate | parametric

Computes variable-lag Granger causality to test if time series X Granger-causes time series Y. Granger-causality defines the causal relation between 2 time series in terms of predictability: X Granger-causes Y if X's past predicts Y's future better than Y's past alone. Variable-lag Granger causality allows X to influence Y with arbitrary instead of fixed time delays. Y is the first object (index = 0) in the time_series array, X the second object (index = 1).

ARGUMENTS

time_series
REQUIREDarray(length: 2)

An array of objects, each representing 1 distinct time series.

reproduction
optionalbooleandefault: false

Return imputed values, applied data transformations and arguments. Useful for reproduction of the results.

precision
optionalobject

Decimal point precision of the output data.

alpha
optionalnumberdefault: 0.05min: 0.01max: 0.1

The statistical significance level of the F-test.

gamma
optionalnumberdefault: 0.5min: 0.01max: 0.99

Critical value to determine whether X Granger-causes Y using Bayesian Information Criterion (BIC) difference ratio.

RETURNS

{
  "alpha": 0.05,
  "gamma": 0.5,
  "reproduction": false,
  "precision": {
    "digits": 4,
    "method": "significant"
  },
  "time_series": [
    {
      "data": {
        "2020-01-01T00:00:00Z": -0.1313,
        "2020-01-01T00:00:01Z": -0.2547,
        "2020-01-01T00:00:02Z": 0.6822,
        "2020-01-01T00:00:03Z": -0.2562,
        "2020-01-01T00:00:04Z": -2.0167,
        "2020-01-01T00:00:05Z": -1.3353,
        "2020-01-01T00:00:06Z": 1.073,
        "2020-01-01T00:00:07Z": 1.0136,
        "2020-01-01T00:00:08Z": 1.1977,
        "2020-01-01T00:00:09Z": 0.0984,
        "2020-01-01T00:00:10Z": 1.0268,
        "2020-01-01T00:00:11Z": -1.0067,
        "2020-01-01T00:00:12Z": -0.5027,
        "2020-01-01T00:00:13Z": -1.3271,
        "2020-01-01T00:00:14Z": -1.3671,
        "2020-01-01T00:00:15Z": -1.7649,
        "2020-01-01T00:00:16Z": 2.1257,
        "2020-01-01T00:00:17Z": 0.3715,
        "2020-01-01T00:00:18Z": -0.0779,
        "2020-01-01T00:00:19Z": -0.5368,
        "2020-01-01T00:00:20Z": 0.4393,
        "2020-01-01T00:00:21Z": -0.5091,
        "2020-01-01T00:00:22Z": -1.3341,
        "2020-01-01T00:00:23Z": 0.0297,
        "2020-01-01T00:00:24Z": -2.0487,
        "2020-01-01T00:00:25Z": 0.1087,
        "2020-01-01T00:00:26Z": -0.0454,
        "2020-01-01T00:00:27Z": 1.7563,
        "2020-01-01T00:00:28Z": 0.1509,
        "2020-01-01T00:00:29Z": 0.5669,
        "2020-01-01T00:00:30Z": 0.6766,
        "2020-01-01T00:00:31Z": -0.7009,
        "2020-01-01T00:00:32Z": 0.7651,
        "2020-01-01T00:00:33Z": 0.1292,
        "2020-01-01T00:00:34Z": -1.277,
        "2020-01-01T00:00:35Z": -0.7001,
        "2020-01-01T00:00:36Z": -0.2866,
        "2020-01-01T00:00:37Z": 0.9069,
        "2020-01-01T00:00:38Z": 0.9477,
        "2020-01-01T00:00:39Z": 0.7532,
        "2020-01-01T00:00:40Z": 0.6888,
        "2020-01-01T00:00:41Z": -0.5163,
        "2020-01-01T00:00:42Z": -1.3712,
        "2020-01-01T00:00:43Z": -1.4961,
        "2020-01-01T00:00:44Z": 1.1132,
        "2020-01-01T00:00:45Z": 1.2232,
        "2020-01-01T00:00:46Z": 2.031,
        "2020-01-01T00:00:47Z": -0.4935,
        "2020-01-01T00:00:48Z": -1.2788,
        "2020-01-01T00:00:49Z": -0.8058,
        "2020-01-01T00:00:50Z": -0.3595,
        "2020-01-01T00:00:51Z": -1.8004,
        "2020-01-01T00:00:52Z": -1.4113,
        "2020-01-01T00:00:53Z": 1.5154,
        "2020-01-01T00:00:54Z": 0.4978,
        "2020-01-01T00:00:55Z": -1.5489,
        "2020-01-01T00:00:56Z": -0.6609,
        "2020-01-01T00:00:57Z": -1.1344,
        "2020-01-01T00:00:58Z": -0.3098,
        "2020-01-01T00:00:59Z": 0.9063,
        "2020-01-01T00:01:00Z": -1.0951,
        "2020-01-01T00:01:01Z": -0.8669,
        "2020-01-01T00:01:02Z": -2.2453,
        "2020-01-01T00:01:03Z": 0.7913,
        "2020-01-01T00:01:04Z": -0.8278,
        "2020-01-01T00:01:05Z": -0.8278,
        "2020-01-01T00:01:06Z": -0.8278,
        "2020-01-01T00:01:07Z": -0.8278,
        "2020-01-01T00:01:08Z": -0.8278,
        "2020-01-01T00:01:09Z": -0.8278,
        "2020-01-01T00:01:10Z": -0.8278,
        "2020-01-01T00:01:11Z": -0.8278,
        "2020-01-01T00:01:12Z": -0.8278,
        "2020-01-01T00:01:13Z": -0.8278,
        "2020-01-01T00:01:14Z": -0.8278,
        "2020-01-01T00:01:15Z": -0.8278,
        "2020-01-01T00:01:16Z": -0.8278,
        "2020-01-01T00:01:17Z": -0.8278,
        "2020-01-01T00:01:18Z": -0.8278,
        "2020-01-01T00:01:19Z": -0.8278,
        "2020-01-01T00:01:20Z": -0.8278,
        "2020-01-01T00:01:21Z": -0.8278,
        "2020-01-01T00:01:22Z": -0.8278,
        "2020-01-01T00:01:23Z": -0.8278,
        "2020-01-01T00:01:24Z": -0.8278,
        "2020-01-01T00:01:25Z": -0.4599,
        "2020-01-01T00:01:26Z": -0.6806,
        "2020-01-01T00:01:27Z": 0.0633,
        "2020-01-01T00:01:28Z": 0.0769,
        "2020-01-01T00:01:29Z": -1.3076,
        "2020-01-01T00:01:30Z": -1.4155,
        "2020-01-01T00:01:31Z": -0.9169,
        "2020-01-01T00:01:32Z": 0.6634,
        "2020-01-01T00:01:33Z": -0.3621,
        "2020-01-01T00:01:34Z": -1.9313,
        "2020-01-01T00:01:35Z": 0.1522,
        "2020-01-01T00:01:36Z": -0.4343,
        "2020-01-01T00:01:37Z": -0.2194,
        "2020-01-01T00:01:38Z": -1.0797,
        "2020-01-01T00:01:39Z": 0.198
      },
      "imputation": {
        "method": "linear",
        "ma_window_size": 10
      },
      "transformations": {
        "box_cox": {
          "apply": false,
          "lambda": "auto",
          "method": "guerrero",
          "upper": 2,
          "lower": -1
        },
        "log": {
          "apply": false,
          "base": "e",
          "factor": null,
          "constant": 1
        },
        "seasonal_diff": {
          "apply": false,
          "period": "auto",
          "n_diffs": "auto",
          "test": "ss",
          "alpha": 0.05
        },
        "first_diff": {
          "apply": false,
          "n_diffs": "auto",
          "test": "kpss",
          "type": "level",
          "alpha": 0.05
        }
      }
    },
    {
      "data": {
        "2020-01-01T00:00:00Z": -1.3487,
        "2020-01-01T00:00:01Z": 1.0557,
        "2020-01-01T00:00:02Z": 1.1499,
        "2020-01-01T00:00:03Z": 1.1876,
        "2020-01-01T00:00:04Z": 0.3059,
        "2020-01-01T00:00:05Z": 0.9625,
        "2020-01-01T00:00:06Z": -1.0361,
        "2020-01-01T00:00:07Z": -0.567,
        "2020-01-01T00:00:08Z": -1.2387,
        "2020-01-01T00:00:09Z": -1.3545,
        "2020-01-01T00:00:10Z": -1.825,
        "2020-01-01T00:00:11Z": 2.0177,
        "2020-01-01T00:00:12Z": 0.5829,
        "2020-01-01T00:00:13Z": -0.1302,
        "2020-01-01T00:00:14Z": -0.3966,
        "2020-01-01T00:00:15Z": 0.4385,
        "2020-01-01T00:00:16Z": -0.3979,
        "2020-01-01T00:00:17Z": -1.3617,
        "2020-01-01T00:00:18Z": 0.0283,
        "2020-01-01T00:00:19Z": -2.0452,
        "2020-01-01T00:00:20Z": 0.1732,
        "2020-01-01T00:00:21Z": -0.082,
        "2020-01-01T00:00:22Z": 1.728,
        "2020-01-01T00:00:23Z": 0.2788,
        "2020-01-01T00:00:24Z": 0.6235,
        "2020-01-01T00:00:25Z": 0.5601,
        "2020-01-01T00:00:26Z": -0.8113,
        "2020-01-01T00:00:27Z": 0.8798,
        "2020-01-01T00:00:28Z": 0.1574,
        "2020-01-01T00:00:29Z": -1.3767,
        "2020-01-01T00:00:30Z": -0.6931,
        "2020-01-01T00:00:31Z": -0.2449,
        "2020-01-01T00:00:32Z": 0.9007,
        "2020-01-01T00:00:33Z": 1.1541,
        "2020-01-01T00:00:34Z": 0.7693,
        "2020-01-01T00:00:35Z": 0.5903,
        "2020-01-01T00:00:36Z": -0.5249,
        "2020-01-01T00:00:37Z": -1.3335,
        "2020-01-01T00:00:38Z": -1.4708,
        "2020-01-01T00:00:39Z": 1.0695,
        "2020-01-01T00:00:40Z": 1.2204,
        "2020-01-01T00:00:41Z": 1.9026,
        "2020-01-01T00:00:42Z": -0.5982,
        "2020-01-01T00:00:43Z": -1.2494,
        "2020-01-01T00:00:44Z": -0.8278,
        "2020-01-01T00:00:45Z": -0.4073,
        "2020-01-01T00:00:46Z": -1.7324,
        "2020-01-01T00:00:47Z": -1.1518,
        "2020-01-01T00:00:48Z": 1.377,
        "2020-01-01T00:00:49Z": 0.5655,
        "2020-01-01T00:00:50Z": -1.3969,
        "2020-01-01T00:00:51Z": -0.5774,
        "2020-01-01T00:00:52Z": -1.0273,
        "2020-01-01T00:00:53Z": -0.4226,
        "2020-01-01T00:00:54Z": 0.8605,
        "2020-01-01T00:00:55Z": -1.1065,
        "2020-01-01T00:00:56Z": -0.6903,
        "2020-01-01T00:00:57Z": -2.263,
        "2020-01-01T00:00:58Z": 0.772,
        "2020-01-01T00:00:59Z": 0.4187,
        "2020-01-01T00:01:00Z": 1.1538,
        "2020-01-01T00:01:01Z": -0.2138,
        "2020-01-01T00:01:02Z": 0.2582,
        "2020-01-01T00:01:03Z": -0.7185,
        "2020-01-01T00:01:04Z": -1.4585,
        "2020-01-01T00:01:05Z": -1.1961,
        "2020-01-01T00:01:06Z": -0.2879,
        "2020-01-01T00:01:07Z": -0.1395,
        "2020-01-01T00:01:08Z": 0.4891,
        "2020-01-01T00:01:09Z": 1.1885,
        "2020-01-01T00:01:10Z": -0.5853,
        "2020-01-01T00:01:11Z": 0.8781,
        "2020-01-01T00:01:12Z": 0.2799,
        "2020-01-01T00:01:13Z": 0.9518,
        "2020-01-01T00:01:14Z": 0.0218,
        "2020-01-01T00:01:15Z": 1.4187,
        "2020-01-01T00:01:16Z": 0.3473,
        "2020-01-01T00:01:17Z": -0.893,
        "2020-01-01T00:01:18Z": -1.3547,
        "2020-01-01T00:01:19Z": 1.16,
        "2020-01-01T00:01:20Z": -0.4298,
        "2020-01-01T00:01:21Z": -0.7005,
        "2020-01-01T00:01:22Z": 0.0798,
        "2020-01-01T00:01:23Z": 0.0346,
        "2020-01-01T00:01:24Z": -1.3268,
        "2020-01-01T00:01:25Z": -1.4621,
        "2020-01-01T00:01:26Z": -0.9852,
        "2020-01-01T00:01:27Z": 0.6201,
        "2020-01-01T00:01:28Z": -0.355,
        "2020-01-01T00:01:29Z": -1.9091,
        "2020-01-01T00:01:30Z": 0.0662,
        "2020-01-01T00:01:31Z": -0.4186,
        "2020-01-01T00:01:32Z": -0.2682,
        "2020-01-01T00:01:33Z": -0.9805,
        "2020-01-01T00:01:34Z": 0.1915,
        "2020-01-01T00:01:35Z": -0.7831,
        "2020-01-01T00:01:36Z": 0,
        "2020-01-01T00:01:37Z": 0,
        "2020-01-01T00:01:38Z": 0,
        "2020-01-01T00:01:39Z": 0
      },
      "imputation": {
        "method": "linear",
        "ma_window_size": 10
      },
      "transformations": {
        "box_cox": {
          "apply": false,
          "lambda": "auto",
          "method": "guerrero",
          "upper": 2,
          "lower": -1
        },
        "log": {
          "apply": false,
          "base": "e",
          "factor": null,
          "constant": 1
        },
        "seasonal_diff": {
          "apply": false,
          "period": "auto",
          "n_diffs": "auto",
          "test": "ss",
          "alpha": 0.05
        },
        "first_diff": {
          "apply": false,
          "n_diffs": "auto",
          "test": "kpss",
          "type": "level",
          "alpha": 0.05
        }
      }
    }
  ]
}
{
  "report": {
    "computation_time": 396.52
  },
  "result": {
    "reproduction": {},
    "data": {
      "max_lag": 5,
      "f_test": {
        "f": 105.5,
        "p_value": 0,
        "x_causes_y": true
      },
      "bic": {
        "h0": 0.9921,
        "h1": 0.1803,
        "diff_ratio": 0.8183,
        "x_causes_y": {
          "h0<h1": true,
          "diff_ratio": true
        }
      }
    }
  }
}
{
  "report": {
    "computation_time": 396.52
  },
  "result": {
    "reproduction": {},
    "data": {
      "max_lag": 5,
      "f_test": {
        "f": 105.5,
        "p_value": 0,
        "x_causes_y": true
      },
      "bic": {
        "h0": 0.9921,
        "h1": 0.1803,
        "diff_ratio": 0.8183,
        "x_causes_y": {
          "h0<h1": true,
          "diff_ratio": true
        }
      }
    }
  }
}
        

matrix profile

POST /invocation/matrix-profile

Recurring pattern detection | Anomaly detection | Chain detection
univariate | nonparametric | fast data

Computes the Matrix Profile and searches for motifs, discords and chains.

Relatively low distance values of the matrix_profile indicate that the subsequence in the original time series must have (at least one) relatively similar subsequence elsewhere in the data (such reoccurring patterns are called motifs). Relatively high distance values of the matrix_profile indicate that the subsequence in the original time series must be unique in its shape (such areas are called discords or anomalies).

Time series chains are motifs that evolve over time.

ARGUMENTS

time_series
REQUIREDarray(length: 1)

An array of objects, each representing 1 distinct time series.

reproduction
optionalbooleandefault: false

Return imputed values, applied data transformations and arguments. Useful for reproduction of the results.

precision
optionalobject

Decimal point precision of the output data.

method
optionalstringdefault: stomp
valid values: stomp, scrimp

stomp is the most widely deployed algorithm for computing the Matrix Profile. scrimp is a newer algorithm that has the anytime property (recommended).

window_size
optionalintegerdefault: 10min: 5

The size of the moving window in number of data points. Changed to window_size = floor(n/2), if window_size > n/2.

exclusion_factor
optionalnumberdefault: 0.5min: 0.1max: 1

Is multiplied with the window_size parameter to produce the exclusion window size. The exclusion window is used to avoid trivial matches.

neighbor_exclusion_radius
optionalintegerdefault: 3min: 1

Is multiplied with the current motif or discord distance to exclude matching neighbors with a larger distance.

n_motifs
optionalintegerdefault: 3min: 1

Number of motifs to detect.

n_motif_neighbors
optionalintegerdefault: 10min: 1

Number of motif neighbors to detect.

n_discords
optionalintegerdefault: 1min: 1

Number of discords to detect.

n_discord_neighbors
optionalintegerdefault: 3min: 1

Number of discord neighbors to detect.

RETURNS

{
  "method": "stomp",
  "window_size": 10,
  "exclusion_factor": 0.5,
  "neighbor_exclusion_radius": 3,
  "n_motifs": 3,
  "n_motif_neighbors": 10,
  "n_discords": 1,
  "n_discord_neighbors": 3,
  "reproduction": false,
  "precision": {
    "digits": 4,
    "method": "significant"
  },
  "time_series": [
    {
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        "2020-01-01T00:00:02Z": 27.6281,
        "2020-01-01T00:00:03Z": 27.0703,
        "2020-01-01T00:00:04Z": 25.7454,
        "2020-01-01T00:00:05Z": 27.0635,
        "2020-01-01T00:00:06Z": 27.9731,
        "2020-01-01T00:00:07Z": 28.1618,
        "2020-01-01T00:00:08Z": 29.5978,
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        "2020-01-01T00:00:16Z": 30.7687,
        "2020-01-01T00:00:17Z": 30.374,
        "2020-01-01T00:00:18Z": 28.1942,
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        "2020-01-01T00:01:39Z": 50.3534
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      "imputation": {
        "method": "linear",
        "ma_window_size": 10
      },
      "transformations": {
        "box_cox": {
          "apply": false,
          "lambda": "auto",
          "method": "guerrero",
          "upper": 2,
          "lower": -1
        },
        "log": {
          "apply": false,
          "base": "e",
          "factor": null,
          "constant": 1
        },
        "seasonal_diff": {
          "apply": false,
          "period": "auto",
          "n_diffs": "auto",
          "test": "ss",
          "alpha": 0.05
        },
        "first_diff": {
          "apply": false,
          "n_diffs": "auto",
          "test": "kpss",
          "type": "level",
          "alpha": 0.05
        }
      }
    }
  ]
}
{
  "report": {
    "computation_time": 392.86
  },
  "result": {
    "reproduction": {},
    "data": {
      "matrix_profile": [
        {
          "t": "2020-01-01T00:00:00Z",
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        },
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          "distance": 0.7389
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        {
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        {
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        {
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        },
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        },
        {
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        {
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        },
        {
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        },
        {
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        },
        {
          "t": "2020-01-01T00:01:06Z",
          "distance": 0.7303
        },
        {
          "t": "2020-01-01T00:01:07Z",
          "distance": 0.7979
        },
        {
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          "distance": 0.9501
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        {
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          "distance": 1.713
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        {
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        {
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        {
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        },
        {
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        },
        {
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        },
        {
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        },
        {
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        },
        {
          "t": "2020-01-01T00:01:17Z",
          "distance": 1.31
        },
        {
          "t": "2020-01-01T00:01:18Z",
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        },
        {
          "t": "2020-01-01T00:01:19Z",
          "distance": 1.906
        },
        {
          "t": "2020-01-01T00:01:20Z",
          "distance": 1.831
        },
        {
          "t": "2020-01-01T00:01:21Z",
          "distance": 1.893
        },
        {
          "t": "2020-01-01T00:01:22Z",
          "distance": 1.177
        },
        {
          "t": "2020-01-01T00:01:23Z",
          "distance": 0.9444
        },
        {
          "t": "2020-01-01T00:01:24Z",
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        },
        {
          "t": "2020-01-01T00:01:25Z",
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        },
        {
          "t": "2020-01-01T00:01:26Z",
          "distance": 1.274
        },
        {
          "t": "2020-01-01T00:01:27Z",
          "distance": 1.49
        },
        {
          "t": "2020-01-01T00:01:28Z",
          "distance": 1.43
        },
        {
          "t": "2020-01-01T00:01:29Z",
          "distance": 1.778
        },
        {
          "t": "2020-01-01T00:01:30Z",
          "distance": 1.738
        },
        {
          "t": "2020-01-01T00:01:31Z",
          "distance": null
        },
        {
          "t": "2020-01-01T00:01:32Z",
          "distance": null
        },
        {
          "t": "2020-01-01T00:01:33Z",
          "distance": null
        },
        {
          "t": "2020-01-01T00:01:34Z",
          "distance": null
        },
        {
          "t": "2020-01-01T00:01:35Z",
          "distance": null
        },
        {
          "t": "2020-01-01T00:01:36Z",
          "distance": null
        },
        {
          "t": "2020-01-01T00:01:37Z",
          "distance": null
        },
        {
          "t": "2020-01-01T00:01:38Z",
          "distance": null
        },
        {
          "t": "2020-01-01T00:01:39Z",
          "distance": null
        }
      ],
      "motifs": [
        {
          "t": [
            "2020-01-01T00:00:42Z",
            "2020-01-01T00:01:05Z"
          ],
          "neighbors": [
            "2020-01-01T00:00:55Z",
            "2020-01-01T00:00:49Z",
            "2020-01-01T00:00:03Z",
            "2020-01-01T00:00:22Z",
            "2020-01-01T00:01:16Z"
          ],
          "window_size": 10
        },
        {
          "t": [
            "2020-01-01T00:00:16Z",
            "2020-01-01T00:01:23Z"
          ],
          "neighbors": [
            "2020-01-01T00:01:12Z",
            "2020-01-01T00:01:29Z"
          ],
          "window_size": 10
        }
      ],
      "discords": [
        {
          "t": [
            "2020-01-01T00:00:32Z"
          ],
          "neighbors": [
            "2020-01-01T00:01:29Z",
            "2020-01-01T00:01:13Z",
            "2020-01-01T00:01:22Z"
          ],
          "window_size": 10
        }
      ],
      "chains": {
        "best": [
          "2020-01-01T00:00:42Z",
          "2020-01-01T00:01:05Z",
          "2020-01-01T00:01:16Z"
        ],
        "all": [
          [
            "2020-01-01T00:00:08Z",
            "2020-01-01T00:01:09Z",
            "2020-01-01T00:01:19Z"
          ],
          [
            "2020-01-01T00:00:42Z",
            "2020-01-01T00:01:05Z",
            "2020-01-01T00:01:16Z"
          ]
        ]
      }
    }
  }
}
{
  "report": {
    "computation_time": 392.86
  },
  "result": {
    "reproduction": {},
    "data": {
      "matrix_profile": [
        {
          "t": "2020-01-01T00:00:00Z",
          "distance": 0.9539
        },
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          "t": "2020-01-01T00:00:02Z",
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        },
        {
          "t": "2020-01-01T00:00:03Z",
          "distance": 0.732
        },
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        },
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        },
        {
          "t": "2020-01-01T00:00:06Z",
          "distance": 0.7389
        },
        {
          "t": "2020-01-01T00:00:07Z",
          "distance": 1.02
        },
        {
          "t": "2020-01-01T00:00:08Z",
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        },
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          "distance": 2.306
        },
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          "t": "2020-01-01T00:00:10Z",
          "distance": 1.92
        },
        {
          "t": "2020-01-01T00:00:11Z",
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        },
        {
          "t": "2020-01-01T00:00:12Z",
          "distance": 1.278
        },
        {
          "t": "2020-01-01T00:00:13Z",
          "distance": 1.274
        },
        {
          "t": "2020-01-01T00:00:14Z",
          "distance": 1.294
        },
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          "t": "2020-01-01T00:00:15Z",
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          "t": "2020-01-01T00:00:16Z",
          "distance": 0.9444
        },
        {
          "t": "2020-01-01T00:00:17Z",
          "distance": 1.1
        },
        {
          "t": "2020-01-01T00:00:18Z",
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        },
        {
          "t": "2020-01-01T00:00:19Z",
          "distance": 1.738
        },
        {
          "t": "2020-01-01T00:00:20Z",
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      ],
      "motifs": [
        {
          "t": [
            "2020-01-01T00:00:42Z",
            "2020-01-01T00:01:05Z"
          ],
          "neighbors": [
            "2020-01-01T00:00:55Z",
            "2020-01-01T00:00:49Z",
            "2020-01-01T00:00:03Z",
            "2020-01-01T00:00:22Z",
            "2020-01-01T00:01:16Z"
          ],
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        {
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            "2020-01-01T00:01:23Z"
          ],
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          "window_size": 10
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      ],
      "discords": [
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            "2020-01-01T00:00:32Z"
          ],
          "neighbors": [
            "2020-01-01T00:01:29Z",
            "2020-01-01T00:01:13Z",
            "2020-01-01T00:01:22Z"
          ],
          "window_size": 10
        }
      ],
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          "2020-01-01T00:01:05Z",
          "2020-01-01T00:01:16Z"
        ],
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            "2020-01-01T00:01:09Z",
            "2020-01-01T00:01:19Z"
          ],
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            "2020-01-01T00:00:42Z",
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        ]
      }
    }
  }
}
        

serial dependence

POST /invocation/serial-dependence

Serial dependency detection
univariate | parametric

Serial dependence provides functions for quantifying the strength of and evidence for linear and nonlinear lag-dependencies.

ARGUMENTS

time_series
REQUIREDarray(length: 1)

An array of objects, each representing 1 distinct time series.

reproduction
optionalbooleandefault: false

Return imputed values, applied data transformations and arguments. Useful for reproduction of the results.

precision
optionalobject

Decimal point precision of the output data.

method
optionalstringdefault: acf
valid values: acf, pacf, adf, rpadf

The method used to detect serial dependencies. acf computes the Autocorrelation Function. pacf computes the Partial Autocorrelation Function. adf computes the Autodependogram Function. rpadf computes the Reproducibility Probability Autodependogram Function.

max_lag
optionalstring | numberdefault: 10*log10(n)min: 1

The maximum lag at which to calculate the serial dependence function. Default is 10*log10(n), where n is the number of observations. Changed to max_lag = n - 1, if max_lag >= n.

alpha
optionalnumberdefault: 0.05min: 0.01max: 0.1

The statistical significance level of the test.

RETURNS

{
  "method": "acf",
  "max_lag": "10*log10(n)",
  "alpha": 0.05,
  "reproduction": false,
  "precision": {
    "digits": 4,
    "method": "significant"
  },
  "time_series": [
    {
      "data": {
        "2020-01-01T00:00:00Z": 28.0137,
        "2020-01-01T00:00:01Z": 27.8591,
        "2020-01-01T00:00:02Z": 27.6281,
        "2020-01-01T00:00:03Z": 27.0703,
        "2020-01-01T00:00:04Z": 25.7454,
        "2020-01-01T00:00:05Z": 27.0635,
        "2020-01-01T00:00:06Z": 27.9731,
        "2020-01-01T00:00:07Z": 28.1618,
        "2020-01-01T00:00:08Z": 29.5978,
        "2020-01-01T00:00:09Z": 30.9978,
        "2020-01-01T00:00:10Z": 31.0237,
        "2020-01-01T00:00:11Z": 31.6535,
        "2020-01-01T00:00:12Z": 32.0346,
        "2020-01-01T00:00:13Z": 31.8492,
        "2020-01-01T00:00:14Z": 32.3419,
        "2020-01-01T00:00:15Z": 32.0351,
        "2020-01-01T00:00:16Z": 30.7687,
        "2020-01-01T00:00:17Z": 30.374,
        "2020-01-01T00:00:18Z": 28.1942,
        "2020-01-01T00:00:19Z": 25.9453,
        "2020-01-01T00:00:20Z": 23.6843,
        "2020-01-01T00:00:21Z": 21.943,
        "2020-01-01T00:00:22Z": 20.309,
        "2020-01-01T00:00:23Z": 19.3427,
        "2020-01-01T00:00:24Z": 19.3478,
        "2020-01-01T00:00:25Z": 19.7972,
        "2020-01-01T00:00:26Z": 21.2299,
        "2020-01-01T00:00:27Z": 22.4813,
        "2020-01-01T00:00:28Z": 23.2128,
        "2020-01-01T00:00:29Z": 22.7081,
        "2020-01-01T00:00:30Z": 23.1786,
        "2020-01-01T00:00:31Z": 22.805,
        "2020-01-01T00:00:32Z": 23.4281,
        "2020-01-01T00:00:33Z": 24.5025,
        "2020-01-01T00:00:34Z": 24.213,
        "2020-01-01T00:00:35Z": 23.3072,
        "2020-01-01T00:00:36Z": 23.7229,
        "2020-01-01T00:00:37Z": 23.1353,
        "2020-01-01T00:00:38Z": 24.0197,
        "2020-01-01T00:00:39Z": 23.3354,
        "2020-01-01T00:00:40Z": 24.171,
        "2020-01-01T00:00:41Z": 23.8188,
        "2020-01-01T00:00:42Z": 24.6172,
        "2020-01-01T00:00:43Z": 24.2777,
        "2020-01-01T00:00:44Z": 24.2283,
        "2020-01-01T00:00:45Z": 25.1955,
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        "2020-01-01T00:01:17Z": 51.8234,
        "2020-01-01T00:01:18Z": 50.2512,
        "2020-01-01T00:01:19Z": 51.0036,
        "2020-01-01T00:01:20Z": 51.9257,
        "2020-01-01T00:01:21Z": 52.5759,
        "2020-01-01T00:01:22Z": 54.1171,
        "2020-01-01T00:01:23Z": 55.4398,
        "2020-01-01T00:01:24Z": 55.5233,
        "2020-01-01T00:01:25Z": 53.8893,
        "2020-01-01T00:01:26Z": 52.8306,
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        "2020-01-01T00:01:28Z": 51.0688,
        "2020-01-01T00:01:29Z": 51.6046,
        "2020-01-01T00:01:30Z": 51.6625,
        "2020-01-01T00:01:31Z": 51.1545,
        "2020-01-01T00:01:32Z": 50.4331,
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      "imputation": {
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        "ma_window_size": 10
      },
      "transformations": {
        "box_cox": {
          "apply": false,
          "lambda": "auto",
          "method": "guerrero",
          "upper": 2,
          "lower": -1
        },
        "log": {
          "apply": false,
          "base": "e",
          "factor": null,
          "constant": 1
        },
        "seasonal_diff": {
          "apply": false,
          "period": "auto",
          "n_diffs": "auto",
          "test": "ss",
          "alpha": 0.05
        },
        "first_diff": {
          "apply": true,
          "n_diffs": 1,
          "test": "kpss",
          "type": "level",
          "alpha": 0.05
        }
      }
    }
  ]
}
{
  "report": {
    "computation_time": 318.13
  },
  "result": {
    "reproduction": {},
    "data": [
      {
        "lag": 1,
        "acf": 0.5279,
        "p_value": 1.503e-7,
        "critical_value": 0.197
      },
      {
        "lag": 2,
        "acf": 0.341,
        "p_value": 0.0006916,
        "critical_value": 0.197
      },
      {
        "lag": 3,
        "acf": 0.1137,
        "p_value": 0.2581,
        "critical_value": 0.197
      },
      {
        "lag": 4,
        "acf": 0.02225,
        "p_value": 0.8248,
        "critical_value": 0.197
      },
      {
        "lag": 5,
        "acf": -0.05863,
        "p_value": 0.5596,
        "critical_value": 0.197
      },
      {
        "lag": 6,
        "acf": 0.0241,
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        "critical_value": 0.197
      },
      {
        "lag": 7,
        "acf": 0.06706,
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        "critical_value": 0.197
      },
      {
        "lag": 8,
        "acf": 0.08365,
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        "critical_value": 0.197
      },
      {
        "lag": 9,
        "acf": 0.0709,
        "p_value": 0.4805,
        "critical_value": 0.197
      },
      {
        "lag": 10,
        "acf": 0.06227,
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        "critical_value": 0.197
      },
      {
        "lag": 11,
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        "critical_value": 0.197
      },
      {
        "lag": 12,
        "acf": 0.07154,
        "p_value": 0.4766,
        "critical_value": 0.197
      },
      {
        "lag": 13,
        "acf": 0.02766,
        "p_value": 0.7831,
        "critical_value": 0.197
      },
      {
        "lag": 14,
        "acf": -0.03609,
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        "critical_value": 0.197
      },
      {
        "lag": 15,
        "acf": 0.04367,
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        "critical_value": 0.197
      },
      {
        "lag": 16,
        "acf": 0.06411,
        "p_value": 0.5236,
        "critical_value": 0.197
      },
      {
        "lag": 17,
        "acf": 0.02122,
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        "critical_value": 0.197
      },
      {
        "lag": 18,
        "acf": 0.0485,
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        "critical_value": 0.197
      },
      {
        "lag": 19,
        "acf": 0.1013,
        "p_value": 0.3133,
        "critical_value": 0.197
      }
    ]
  }
}
{
  "report": {
    "computation_time": 318.13
  },
  "result": {
    "reproduction": {},
    "data": [
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        "lag": 1,
        "acf": 0.5279,
        "p_value": 1.503e-7,
        "critical_value": 0.197
      },
      {
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        "p_value": 0.0006916,
        "critical_value": 0.197
      },
      {
        "lag": 3,
        "acf": 0.1137,
        "p_value": 0.2581,
        "critical_value": 0.197
      },
      {
        "lag": 4,
        "acf": 0.02225,
        "p_value": 0.8248,
        "critical_value": 0.197
      },
      {
        "lag": 5,
        "acf": -0.05863,
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        "critical_value": 0.197
      },
      {
        "lag": 6,
        "acf": 0.0241,
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        "critical_value": 0.197
      },
      {
        "lag": 7,
        "acf": 0.06706,
        "p_value": 0.5046,
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      {
        "lag": 8,
        "acf": 0.08365,
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      },
      {
        "lag": 9,
        "acf": 0.0709,
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        "critical_value": 0.197
      },
      {
        "lag": 10,
        "acf": 0.06227,
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        "critical_value": 0.197
      },
      {
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      {
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        "acf": 0.07154,
        "p_value": 0.4766,
        "critical_value": 0.197
      },
      {
        "lag": 13,
        "acf": 0.02766,
        "p_value": 0.7831,
        "critical_value": 0.197
      },
      {
        "lag": 14,
        "acf": -0.03609,
        "p_value": 0.7195,
        "critical_value": 0.197
      },
      {
        "lag": 15,
        "acf": 0.04367,
        "p_value": 0.6639,
        "critical_value": 0.197
      },
      {
        "lag": 16,
        "acf": 0.06411,
        "p_value": 0.5236,
        "critical_value": 0.197
      },
      {
        "lag": 17,
        "acf": 0.02122,
        "p_value": 0.8328,
        "critical_value": 0.197
      },
      {
        "lag": 18,
        "acf": 0.0485,
        "p_value": 0.6294,
        "critical_value": 0.197
      },
      {
        "lag": 19,
        "acf": 0.1013,
        "p_value": 0.3133,
        "critical_value": 0.197
      }
    ]
  }
}
        

spectral density

POST /invocation/spectral-density

Spectral analysis
univariate | parametric

Estimates the spectral density of the time series via nonparametric models.

ARGUMENTS

time_series
REQUIREDarray(length: 1)

An array of objects, each representing 1 distinct time series.

reproduction
optionalbooleandefault: false

Return imputed values, applied data transformations and arguments. Useful for reproduction of the results.

precision
optionalobject

Decimal point precision of the output data.

method
optionalstringdefault: direct
valid values: direct, multitaper, wosa

The method for estimating the spectral density. direct estimates the direct spectrum. multitaper implements a multitaper estimation. wosa implements Welch's Overlapped Segment Averaging.

taper
optionalstringdefault: rectangle
valid values: blackman, born_jordan, chebyshev, daniell, dpss, gaussian, hamming, hanning, kaiser, nuttall, papoulis, parzen, raised_cosine, rectangle, sine, triangle

The applied taper. The Discrete Prolate Spheroidal Sequences dpss taper and the sinusoidal sine taper must be used with method = multitaper.

center
optionalbooleandefault: true

Recenter the mean of the time series prior to estimating the spectral density.

conversion
optionalnull | string

Conversion of the spectral density. If null, a conversion is not applied. If decibel, the spectrum is converted to dB via 10 * log10(x).

RETURNS

{
  "method": "direct",
  "taper": "rectangle",
  "center": true,
  "conversion": null,
  "reproduction": false,
  "precision": {
    "digits": 4,
    "method": "significant"
  },
  "time_series": [
    {
      "data": {
        "2020-01-01T00:00:00Z": 28.0137,
        "2020-01-01T00:00:01Z": 27.8591,
        "2020-01-01T00:00:02Z": 27.6281,
        "2020-01-01T00:00:03Z": 27.0703,
        "2020-01-01T00:00:04Z": 25.7454,
        "2020-01-01T00:00:05Z": 27.0635,
        "2020-01-01T00:00:06Z": 27.9731,
        "2020-01-01T00:00:07Z": 28.1618,
        "2020-01-01T00:00:08Z": 29.5978,
        "2020-01-01T00:00:09Z": 30.9978,
        "2020-01-01T00:00:10Z": 31.0237,
        "2020-01-01T00:00:11Z": 31.6535,
        "2020-01-01T00:00:12Z": 32.0346,
        "2020-01-01T00:00:13Z": 31.8492,
        "2020-01-01T00:00:14Z": 32.3419,
        "2020-01-01T00:00:15Z": 32.0351,
        "2020-01-01T00:00:16Z": 30.7687,
        "2020-01-01T00:00:17Z": 30.374,
        "2020-01-01T00:00:18Z": 28.1942,
        "2020-01-01T00:00:19Z": 25.9453,
        "2020-01-01T00:00:20Z": 23.6843,
        "2020-01-01T00:00:21Z": 21.943,
        "2020-01-01T00:00:22Z": 20.309,
        "2020-01-01T00:00:23Z": 19.3427,
        "2020-01-01T00:00:24Z": 19.3478,
        "2020-01-01T00:00:25Z": 19.7972,
        "2020-01-01T00:00:26Z": 21.2299,
        "2020-01-01T00:00:27Z": 22.4813,
        "2020-01-01T00:00:28Z": 23.2128,
        "2020-01-01T00:00:29Z": 22.7081,
        "2020-01-01T00:00:30Z": 23.1786,
        "2020-01-01T00:00:31Z": 22.805,
        "2020-01-01T00:00:32Z": 23.4281,
        "2020-01-01T00:00:33Z": 24.5025,
        "2020-01-01T00:00:34Z": 24.213,
        "2020-01-01T00:00:35Z": 23.3072,
        "2020-01-01T00:00:36Z": 23.7229,
        "2020-01-01T00:00:37Z": 23.1353,
        "2020-01-01T00:00:38Z": 24.0197,
        "2020-01-01T00:00:39Z": 23.3354,
        "2020-01-01T00:00:40Z": 24.171,
        "2020-01-01T00:00:41Z": 23.8188,
        "2020-01-01T00:00:42Z": 24.6172,
        "2020-01-01T00:00:43Z": 24.2777,
        "2020-01-01T00:00:44Z": 24.2283,
        "2020-01-01T00:00:45Z": 25.1955,
        "2020-01-01T00:00:46Z": 26.4958,
        "2020-01-01T00:00:47Z": 28.3069,
        "2020-01-01T00:00:48Z": 29.7687,
        "2020-01-01T00:00:49Z": 30.9865,
        "2020-01-01T00:00:50Z": 29.7695,
        "2020-01-01T00:00:51Z": 30.1204,
        "2020-01-01T00:00:52Z": 31.742,
        "2020-01-01T00:00:53Z": 34.6089,
        "2020-01-01T00:00:54Z": 36.054,
        "2020-01-01T00:00:55Z": 36.3756,
        "2020-01-01T00:00:56Z": 37.36,
        "2020-01-01T00:00:57Z": 38.1193,
        "2020-01-01T00:00:58Z": 38.5563,
        "2020-01-01T00:00:59Z": 40.6662,
        "2020-01-01T00:01:00Z": 42.6862,
        "2020-01-01T00:01:01Z": 45.0665,
        "2020-01-01T00:01:02Z": 46.3616,
        "2020-01-01T00:01:03Z": 46.8506,
        "2020-01-01T00:01:04Z": 47.7675,
        "2020-01-01T00:01:05Z": 47.6054,
        "2020-01-01T00:01:06Z": 46.2565,
        "2020-01-01T00:01:07Z": 45.536,
        "2020-01-01T00:01:08Z": 46.3415,
        "2020-01-01T00:01:09Z": 48.0423,
        "2020-01-01T00:01:10Z": 50.8812,
        "2020-01-01T00:01:11Z": 52.6965,
        "2020-01-01T00:01:12Z": 54.7823,
        "2020-01-01T00:01:13Z": 53.512,
        "2020-01-01T00:01:14Z": 53.2565,
        "2020-01-01T00:01:15Z": 53.0911,
        "2020-01-01T00:01:16Z": 52.4152,
        "2020-01-01T00:01:17Z": 51.8234,
        "2020-01-01T00:01:18Z": 50.2512,
        "2020-01-01T00:01:19Z": 51.0036,
        "2020-01-01T00:01:20Z": 51.9257,
        "2020-01-01T00:01:21Z": 52.5759,
        "2020-01-01T00:01:22Z": 54.1171,
        "2020-01-01T00:01:23Z": 55.4398,
        "2020-01-01T00:01:24Z": 55.5233,
        "2020-01-01T00:01:25Z": 53.8893,
        "2020-01-01T00:01:26Z": 52.8306,
        "2020-01-01T00:01:27Z": 52.2715,
        "2020-01-01T00:01:28Z": 51.0688,
        "2020-01-01T00:01:29Z": 51.6046,
        "2020-01-01T00:01:30Z": 51.6625,
        "2020-01-01T00:01:31Z": 51.1545,
        "2020-01-01T00:01:32Z": 50.4331,
        "2020-01-01T00:01:33Z": 49.8225,
        "2020-01-01T00:01:34Z": 47.5345,
        "2020-01-01T00:01:35Z": 48.5842,
        "2020-01-01T00:01:36Z": 49.3886,
        "2020-01-01T00:01:37Z": 50.4767,
        "2020-01-01T00:01:38Z": 49.5141,
        "2020-01-01T00:01:39Z": 50.3534
      },
      "imputation": {
        "method": "linear",
        "ma_window_size": 10
      },
      "transformations": {
        "box_cox": {
          "apply": false,
          "lambda": "auto",
          "method": "guerrero",
          "upper": 2,
          "lower": -1
        },
        "log": {
          "apply": false,
          "base": "e",
          "factor": null,
          "constant": 1
        },
        "seasonal_diff": {
          "apply": false,
          "period": "auto",
          "n_diffs": "auto",
          "test": "ss",
          "alpha": 0.05
        },
        "first_diff": {
          "apply": true,
          "n_diffs": 1,
          "test": "kpss",
          "type": "level",
          "alpha": 0.05
        }
      }
    }
  ]
}
{
  "report": {
    "computation_time": 506.74
  },
  "result": {
    "reproduction": {},
    "data": [
      {
        "frequency": 0.005051,
        "spectral_density": 1.549
      },
      {
        "frequency": 0.0101,
        "spectral_density": 9.125
      },
      {
        "frequency": 0.01515,
        "spectral_density": 11.73
      },
      {
        "frequency": 0.0202,
        "spectral_density": 3.564
      },
      {
        "frequency": 0.02525,
        "spectral_density": 0.04576
      },
      {
        "frequency": 0.0303,
        "spectral_density": 1.133
      },
      {
        "frequency": 0.03535,
        "spectral_density": 0.7654
      },
      {
        "frequency": 0.0404,
        "spectral_density": 4.3
      },
      {
        "frequency": 0.04545,
        "spectral_density": 4.009
      },
      {
        "frequency": 0.05051,
        "spectral_density": 2.597
      },
      {
        "frequency": 0.05556,
        "spectral_density": 5.287
      },
      {
        "frequency": 0.06061,
        "spectral_density": 1.901
      },
      {
        "frequency": 0.06566,
        "spectral_density": 3.104
      },
      {
        "frequency": 0.07071,
        "spectral_density": 3.804
      },
      {
        "frequency": 0.07576,
        "spectral_density": 0.4697
      },
      {
        "frequency": 0.08081,
        "spectral_density": 2.092
      },
      {
        "frequency": 0.08586,
        "spectral_density": 3.631
      },
      {
        "frequency": 0.09091,
        "spectral_density": 4.136
      },
      {
        "frequency": 0.09596,
        "spectral_density": 3.043
      },
      {
        "frequency": 0.101,
        "spectral_density": 0.8781
      },
      {
        "frequency": 0.1061,
        "spectral_density": 4.862
      },
      {
        "frequency": 0.1111,
        "spectral_density": 6.586
      },
      {
        "frequency": 0.1162,
        "spectral_density": 1.42
      },
      {
        "frequency": 0.1212,
        "spectral_density": 1.219
      },
      {
        "frequency": 0.1263,
        "spectral_density": 1.059
      },
      {
        "frequency": 0.1313,
        "spectral_density": 1.191
      },
      {
        "frequency": 0.1364,
        "spectral_density": 2.433
      },
      {
        "frequency": 0.1414,
        "spectral_density": 3.431
      },
      {
        "frequency": 0.1465,
        "spectral_density": 2.293
      },
      {
        "frequency": 0.1515,
        "spectral_density": 0.01837
      },
      {
        "frequency": 0.1566,
        "spectral_density": 1.504
      },
      {
        "frequency": 0.1616,
        "spectral_density": 1.57
      },
      {
        "frequency": 0.1667,
        "spectral_density": 1.047
      },
      {
        "frequency": 0.1717,
        "spectral_density": 0.7104
      },
      {
        "frequency": 0.1768,
        "spectral_density": 0.4123
      },
      {
        "frequency": 0.1818,
        "spectral_density": 0.9853
      },
      {
        "frequency": 0.1869,
        "spectral_density": 2.023
      },
      {
        "frequency": 0.1919,
        "spectral_density": 1.022
      },
      {
        "frequency": 0.197,
        "spectral_density": 0.01258
      },
      {
        "frequency": 0.202,
        "spectral_density": 0.2866
      },
      {
        "frequency": 0.2071,
        "spectral_density": 0.3345
      },
      {
        "frequency": 0.2121,
        "spectral_density": 0.1476
      },
      {
        "frequency": 0.2172,
        "spectral_density": 0.1429
      },
      {
        "frequency": 0.2222,
        "spectral_density": 0.159
      },
      {
        "frequency": 0.2273,
        "spectral_density": 0.4337
      },
      {
        "frequency": 0.2323,
        "spectral_density": 0.7404
      },
      {
        "frequency": 0.2374,
        "spectral_density": 0.0761
      },
      {
        "frequency": 0.2424,
        "spectral_density": 0.2144
      },
      {
        "frequency": 0.2475,
        "spectral_density": 0.1076
      },
      {
        "frequency": 0.2525,
        "spectral_density": 1.785
      },
      {
        "frequency": 0.2576,
        "spectral_density": 1.853
      },
      {
        "frequency": 0.2626,
        "spectral_density": 0.3996
      },
      {
        "frequency": 0.2677,
        "spectral_density": 0.2999
      },
      {
        "frequency": 0.2727,
        "spectral_density": 0.7297
      },
      {
        "frequency": 0.2778,
        "spectral_density": 0.3207
      },
      {
        "frequency": 0.2828,
        "spectral_density": 0.2384
      },
      {
        "frequency": 0.2879,
        "spectral_density": 0.4019
      },
      {
        "frequency": 0.2929,
        "spectral_density": 0.2238
      },
      {
        "frequency": 0.298,
        "spectral_density": 0.907
      },
      {
        "frequency": 0.303,
        "spectral_density": 0.2247
      },
      {
        "frequency": 0.3081,
        "spectral_density": 0.3227
      },
      {
        "frequency": 0.3131,
        "spectral_density": 0.04052
      },
      {
        "frequency": 0.3182,
        "spectral_density": 1.709
      },
      {
        "frequency": 0.3232,
        "spectral_density": 1.069
      },
      {
        "frequency": 0.3283,
        "spectral_density": 0.2678
      },
      {
        "frequency": 0.3333,
        "spectral_density": 1.287
      },
      {
        "frequency": 0.3384,
        "spectral_density": 0.2397
      },
      {
        "frequency": 0.3434,
        "spectral_density": 0.1419
      },
      {
        "frequency": 0.3485,
        "spectral_density": 0.09323
      },
      {
        "frequency": 0.3535,
        "spectral_density": 0.3102
      },
      {
        "frequency": 0.3586,
        "spectral_density": 0.4089
      },
      {
        "frequency": 0.3636,
        "spectral_density": 0.1317
      },
      {
        "frequency": 0.3687,
        "spectral_density": 0.178
      },
      {
        "frequency": 0.3737,
        "spectral_density": 0.3101
      },
      {
        "frequency": 0.3788,
        "spectral_density": 0.5185
      },
      {
        "frequency": 0.3838,
        "spectral_density": 0.6604
      },
      {
        "frequency": 0.3889,
        "spectral_density": 0.7454
      },
      {
        "frequency": 0.3939,
        "spectral_density": 0.5026
      },
      {
        "frequency": 0.399,
        "spectral_density": 0.3033
      },
      {
        "frequency": 0.404,
        "spectral_density": 0.525
      },
      {
        "frequency": 0.4091,
        "spectral_density": 0.1882
      },
      {
        "frequency": 0.4141,
        "spectral_density": 0.06768
      },
      {
        "frequency": 0.4192,
        "spectral_density": 0.02874
      },
      {
        "frequency": 0.4242,
        "spectral_density": 0.09464
      },
      {
        "frequency": 0.4293,
        "spectral_density": 0.7093
      },
      {
        "frequency": 0.4343,
        "spectral_density": 1.608
      },
      {
        "frequency": 0.4394,
        "spectral_density": 0.7455
      },
      {
        "frequency": 0.4444,
        "spectral_density": 0.1824
      },
      {
        "frequency": 0.4495,
        "spectral_density": 0.08049
      },
      {
        "frequency": 0.4545,
        "spectral_density": 0.298
      },
      {
        "frequency": 0.4596,
        "spectral_density": 0.3446
      },
      {
        "frequency": 0.4646,
        "spectral_density": 0.06144
      },
      {
        "frequency": 0.4697,
        "spectral_density": 0.8286
      },
      {
        "frequency": 0.4747,
        "spectral_density": 2.355
      },
      {
        "frequency": 0.4798,
        "spectral_density": 1.172
      },
      {
        "frequency": 0.4848,
        "spectral_density": 0.05819
      },
      {
        "frequency": 0.4899,
        "spectral_density": 0.9639
      },
      {
        "frequency": 0.4949,
        "spectral_density": 0.3553
      },
      {
        "frequency": 0.5,
        "spectral_density": 0.09484
      }
    ]
  }
}
{
  "report": {
    "computation_time": 506.74
  },
  "result": {
    "reproduction": {},
    "data": [
      {
        "frequency": 0.005051,
        "spectral_density": 1.549
      },
      {
        "frequency": 0.0101,
        "spectral_density": 9.125
      },
      {
        "frequency": 0.01515,
        "spectral_density": 11.73
      },
      {
        "frequency": 0.0202,
        "spectral_density": 3.564
      },
      {
        "frequency": 0.02525,
        "spectral_density": 0.04576
      },
      {
        "frequency": 0.0303,
        "spectral_density": 1.133
      },
      {
        "frequency": 0.03535,
        "spectral_density": 0.7654
      },
      {
        "frequency": 0.0404,
        "spectral_density": 4.3
      },
      {
        "frequency": 0.04545,
        "spectral_density": 4.009
      },
      {
        "frequency": 0.05051,
        "spectral_density": 2.597
      },
      {
        "frequency": 0.05556,
        "spectral_density": 5.287
      },
      {
        "frequency": 0.06061,
        "spectral_density": 1.901
      },
      {
        "frequency": 0.06566,
        "spectral_density": 3.104
      },
      {
        "frequency": 0.07071,
        "spectral_density": 3.804
      },
      {
        "frequency": 0.07576,
        "spectral_density": 0.4697
      },
      {
        "frequency": 0.08081,
        "spectral_density": 2.092
      },
      {
        "frequency": 0.08586,
        "spectral_density": 3.631
      },
      {
        "frequency": 0.09091,
        "spectral_density": 4.136
      },
      {
        "frequency": 0.09596,
        "spectral_density": 3.043
      },
      {
        "frequency": 0.101,
        "spectral_density": 0.8781
      },
      {
        "frequency": 0.1061,
        "spectral_density": 4.862
      },
      {
        "frequency": 0.1111,
        "spectral_density": 6.586
      },
      {
        "frequency": 0.1162,
        "spectral_density": 1.42
      },
      {
        "frequency": 0.1212,
        "spectral_density": 1.219
      },
      {
        "frequency": 0.1263,
        "spectral_density": 1.059
      },
      {
        "frequency": 0.1313,
        "spectral_density": 1.191
      },
      {
        "frequency": 0.1364,
        "spectral_density": 2.433
      },
      {
        "frequency": 0.1414,
        "spectral_density": 3.431
      },
      {
        "frequency": 0.1465,
        "spectral_density": 2.293
      },
      {
        "frequency": 0.1515,
        "spectral_density": 0.01837
      },
      {
        "frequency": 0.1566,
        "spectral_density": 1.504
      },
      {
        "frequency": 0.1616,
        "spectral_density": 1.57
      },
      {
        "frequency": 0.1667,
        "spectral_density": 1.047
      },
      {
        "frequency": 0.1717,
        "spectral_density": 0.7104
      },
      {
        "frequency": 0.1768,
        "spectral_density": 0.4123
      },
      {
        "frequency": 0.1818,
        "spectral_density": 0.9853
      },
      {
        "frequency": 0.1869,
        "spectral_density": 2.023
      },
      {
        "frequency": 0.1919,
        "spectral_density": 1.022
      },
      {
        "frequency": 0.197,
        "spectral_density": 0.01258
      },
      {
        "frequency": 0.202,
        "spectral_density": 0.2866
      },
      {
        "frequency": 0.2071,
        "spectral_density": 0.3345
      },
      {
        "frequency": 0.2121,
        "spectral_density": 0.1476
      },
      {
        "frequency": 0.2172,
        "spectral_density": 0.1429
      },
      {
        "frequency": 0.2222,
        "spectral_density": 0.159
      },
      {
        "frequency": 0.2273,
        "spectral_density": 0.4337
      },
      {
        "frequency": 0.2323,
        "spectral_density": 0.7404
      },
      {
        "frequency": 0.2374,
        "spectral_density": 0.0761
      },
      {
        "frequency": 0.2424,
        "spectral_density": 0.2144
      },
      {
        "frequency": 0.2475,
        "spectral_density": 0.1076
      },
      {
        "frequency": 0.2525,
        "spectral_density": 1.785
      },
      {
        "frequency": 0.2576,
        "spectral_density": 1.853
      },
      {
        "frequency": 0.2626,
        "spectral_density": 0.3996
      },
      {
        "frequency": 0.2677,
        "spectral_density": 0.2999
      },
      {
        "frequency": 0.2727,
        "spectral_density": 0.7297
      },
      {
        "frequency": 0.2778,
        "spectral_density": 0.3207
      },
      {
        "frequency": 0.2828,
        "spectral_density": 0.2384
      },
      {
        "frequency": 0.2879,
        "spectral_density": 0.4019
      },
      {
        "frequency": 0.2929,
        "spectral_density": 0.2238
      },
      {
        "frequency": 0.298,
        "spectral_density": 0.907
      },
      {
        "frequency": 0.303,
        "spectral_density": 0.2247
      },
      {
        "frequency": 0.3081,
        "spectral_density": 0.3227
      },
      {
        "frequency": 0.3131,
        "spectral_density": 0.04052
      },
      {
        "frequency": 0.3182,
        "spectral_density": 1.709
      },
      {
        "frequency": 0.3232,
        "spectral_density": 1.069
      },
      {
        "frequency": 0.3283,
        "spectral_density": 0.2678
      },
      {
        "frequency": 0.3333,
        "spectral_density": 1.287
      },
      {
        "frequency": 0.3384,
        "spectral_density": 0.2397
      },
      {
        "frequency": 0.3434,
        "spectral_density": 0.1419
      },
      {
        "frequency": 0.3485,
        "spectral_density": 0.09323
      },
      {
        "frequency": 0.3535,
        "spectral_density": 0.3102
      },
      {
        "frequency": 0.3586,
        "spectral_density": 0.4089
      },
      {
        "frequency": 0.3636,
        "spectral_density": 0.1317
      },
      {
        "frequency": 0.3687,
        "spectral_density": 0.178
      },
      {
        "frequency": 0.3737,
        "spectral_density": 0.3101
      },
      {
        "frequency": 0.3788,
        "spectral_density": 0.5185
      },
      {
        "frequency": 0.3838,
        "spectral_density": 0.6604
      },
      {
        "frequency": 0.3889,
        "spectral_density": 0.7454
      },
      {
        "frequency": 0.3939,
        "spectral_density": 0.5026
      },
      {
        "frequency": 0.399,
        "spectral_density": 0.3033
      },
      {
        "frequency": 0.404,
        "spectral_density": 0.525
      },
      {
        "frequency": 0.4091,
        "spectral_density": 0.1882
      },
      {
        "frequency": 0.4141,
        "spectral_density": 0.06768
      },
      {
        "frequency": 0.4192,
        "spectral_density": 0.02874
      },
      {
        "frequency": 0.4242,
        "spectral_density": 0.09464
      },
      {
        "frequency": 0.4293,
        "spectral_density": 0.7093
      },
      {
        "frequency": 0.4343,
        "spectral_density": 1.608
      },
      {
        "frequency": 0.4394,
        "spectral_density": 0.7455
      },
      {
        "frequency": 0.4444,
        "spectral_density": 0.1824
      },
      {
        "frequency": 0.4495,
        "spectral_density": 0.08049
      },
      {
        "frequency": 0.4545,
        "spectral_density": 0.298
      },
      {
        "frequency": 0.4596,
        "spectral_density": 0.3446
      },
      {
        "frequency": 0.4646,
        "spectral_density": 0.06144
      },
      {
        "frequency": 0.4697,
        "spectral_density": 0.8286
      },
      {
        "frequency": 0.4747,
        "spectral_density": 2.355
      },
      {
        "frequency": 0.4798,
        "spectral_density": 1.172
      },
      {
        "frequency": 0.4848,
        "spectral_density": 0.05819
      },
      {
        "frequency": 0.4899,
        "spectral_density": 0.9639
      },
      {
        "frequency": 0.4949,
        "spectral_density": 0.3553
      },
      {
        "frequency": 0.5,
        "spectral_density": 0.09484
      }
    ]
  }
}
        

spectral entropy

POST /invocation/spectral-entropy

Spectral analysis
univariate | parametric | fast data

Estimates the spectral Shannon entropy from the normalized spectral density within a moving window along the time series. The Omega forecastability measure is defined as 1 - spectral entropy, thus an increase in spectral entropy corresponds to a decrease in forecastability.

ARGUMENTS

time_series
REQUIREDarray(length: 1)

An array of objects, each representing 1 distinct time series.

reproduction
optionalbooleandefault: false

Return imputed values, applied data transformations and arguments. Useful for reproduction of the results.

precision
optionalobject

Decimal point precision of the output data.

method
optionalstringdefault: direct
valid values: direct, multitaper, wosa

The method for estimating the spectral density. direct estimates the direct spectrum. multitaper implements a multitaper estimation. wosa implements Welch's Overlapped Segment Averaging.

taper
optionalstringdefault: rectangle
valid values: blackman, born_jordan, chebyshev, daniell, dpss, gaussian, hamming, hanning, kaiser, nuttall, papoulis, parzen, raised_cosine, rectangle, sine, triangle

The applied taper. The Discrete Prolate Spheroidal Sequences dpss taper and the sinusoidal sine taper must be used with method = multitaper.

window_size
optionalintegerdefault: 10min: 10

The size of the moving window in number of data points. Changed to window_size = floor(n/2), if window_size > n/2.

RETURNS

{
  "method": "direct",
  "taper": "rectangle",
  "window_size": 10,
  "reproduction": false,
  "precision": {
    "digits": 4,
    "method": "significant"
  },
  "time_series": [
    {
      "data": {
        "2020-01-01T00:00:00Z": 28.0137,
        "2020-01-01T00:00:01Z": 27.8591,
        "2020-01-01T00:00:02Z": 27.6281,
        "2020-01-01T00:00:03Z": 27.0703,
        "2020-01-01T00:00:04Z": 25.7454,
        "2020-01-01T00:00:05Z": 27.0635,
        "2020-01-01T00:00:06Z": 27.9731,
        "2020-01-01T00:00:07Z": 28.1618,
        "2020-01-01T00:00:08Z": 29.5978,
        "2020-01-01T00:00:09Z": 30.9978,
        "2020-01-01T00:00:10Z": 31.0237,
        "2020-01-01T00:00:11Z": 31.6535,
        "2020-01-01T00:00:12Z": 32.0346,
        "2020-01-01T00:00:13Z": 31.8492,
        "2020-01-01T00:00:14Z": 32.3419,
        "2020-01-01T00:00:15Z": 32.0351,
        "2020-01-01T00:00:16Z": 30.7687,
        "2020-01-01T00:00:17Z": 30.374,
        "2020-01-01T00:00:18Z": 28.1942,
        "2020-01-01T00:00:19Z": 25.9453,
        "2020-01-01T00:00:20Z": 23.6843,
        "2020-01-01T00:00:21Z": 21.943,
        "2020-01-01T00:00:22Z": 20.309,
        "2020-01-01T00:00:23Z": 19.3427,
        "2020-01-01T00:00:24Z": 19.3478,
        "2020-01-01T00:00:25Z": 19.7972,
        "2020-01-01T00:00:26Z": 21.2299,
        "2020-01-01T00:00:27Z": 22.4813,
        "2020-01-01T00:00:28Z": 23.2128,
        "2020-01-01T00:00:29Z": 22.7081,
        "2020-01-01T00:00:30Z": 23.1786,
        "2020-01-01T00:00:31Z": 22.805,
        "2020-01-01T00:00:32Z": 23.4281,
        "2020-01-01T00:00:33Z": 24.5025,
        "2020-01-01T00:00:34Z": 24.213,
        "2020-01-01T00:00:35Z": 23.3072,
        "2020-01-01T00:00:36Z": 23.7229,
        "2020-01-01T00:00:37Z": 23.1353,
        "2020-01-01T00:00:38Z": 24.0197,
        "2020-01-01T00:00:39Z": 23.3354,
        "2020-01-01T00:00:40Z": 24.171,
        "2020-01-01T00:00:41Z": 23.8188,
        "2020-01-01T00:00:42Z": 24.6172,
        "2020-01-01T00:00:43Z": 24.2777,
        "2020-01-01T00:00:44Z": 24.2283,
        "2020-01-01T00:00:45Z": 25.1955,
        "2020-01-01T00:00:46Z": 26.4958,
        "2020-01-01T00:00:47Z": 28.3069,
        "2020-01-01T00:00:48Z": 29.7687,
        "2020-01-01T00:00:49Z": 30.9865,
        "2020-01-01T00:00:50Z": 29.7695,
        "2020-01-01T00:00:51Z": 30.1204,
        "2020-01-01T00:00:52Z": 31.742,
        "2020-01-01T00:00:53Z": 34.6089,
        "2020-01-01T00:00:54Z": 36.054,
        "2020-01-01T00:00:55Z": 36.3756,
        "2020-01-01T00:00:56Z": 37.36,
        "2020-01-01T00:00:57Z": 38.1193,
        "2020-01-01T00:00:58Z": 38.5563,
        "2020-01-01T00:00:59Z": 40.6662,
        "2020-01-01T00:01:00Z": 42.6862,
        "2020-01-01T00:01:01Z": 45.0665,
        "2020-01-01T00:01:02Z": 46.3616,
        "2020-01-01T00:01:03Z": 46.8506,
        "2020-01-01T00:01:04Z": 47.7675,
        "2020-01-01T00:01:05Z": 47.6054,
        "2020-01-01T00:01:06Z": 46.2565,
        "2020-01-01T00:01:07Z": 45.536,
        "2020-01-01T00:01:08Z": 46.3415,
        "2020-01-01T00:01:09Z": 48.0423,
        "2020-01-01T00:01:10Z": 50.8812,
        "2020-01-01T00:01:11Z": 52.6965,
        "2020-01-01T00:01:12Z": 54.7823,
        "2020-01-01T00:01:13Z": 53.512,
        "2020-01-01T00:01:14Z": 53.2565,
        "2020-01-01T00:01:15Z": 53.0911,
        "2020-01-01T00:01:16Z": 52.4152,
        "2020-01-01T00:01:17Z": 51.8234,
        "2020-01-01T00:01:18Z": 50.2512,
        "2020-01-01T00:01:19Z": 51.0036,
        "2020-01-01T00:01:20Z": 51.9257,
        "2020-01-01T00:01:21Z": 52.5759,
        "2020-01-01T00:01:22Z": 54.1171,
        "2020-01-01T00:01:23Z": 55.4398,
        "2020-01-01T00:01:24Z": 55.5233,
        "2020-01-01T00:01:25Z": 53.8893,
        "2020-01-01T00:01:26Z": 52.8306,
        "2020-01-01T00:01:27Z": 52.2715,
        "2020-01-01T00:01:28Z": 51.0688,
        "2020-01-01T00:01:29Z": 51.6046,
        "2020-01-01T00:01:30Z": 51.6625,
        "2020-01-01T00:01:31Z": 51.1545,
        "2020-01-01T00:01:32Z": 50.4331,
        "2020-01-01T00:01:33Z": 49.8225,
        "2020-01-01T00:01:34Z": 47.5345,
        "2020-01-01T00:01:35Z": 48.5842,
        "2020-01-01T00:01:36Z": 49.3886,
        "2020-01-01T00:01:37Z": 50.4767,
        "2020-01-01T00:01:38Z": 49.5141,
        "2020-01-01T00:01:39Z": 50.3534
      },
      "imputation": {
        "method": "linear",
        "ma_window_size": 10
      },
      "transformations": {
        "box_cox": {
          "apply": false,
          "lambda": "auto",
          "method": "guerrero",
          "upper": 2,
          "lower": -1
        },
        "log": {
          "apply": false,
          "base": "e",
          "factor": null,
          "constant": 1
        },
        "seasonal_diff": {
          "apply": false,
          "period": "auto",
          "n_diffs": "auto",
          "test": "ss",
          "alpha": 0.05
        },
        "first_diff": {
          "apply": true,
          "n_diffs": 1,
          "test": "kpss",
          "type": "level",
          "alpha": 0.05
        }
      }
    }
  ]
}
{
  "report": {
    "computation_time": 725.65
  },
  "result": {
    "reproduction": {},
    "data": [
      {
        "t": "2020-01-01T00:00:00Z",
        "spectral_entropy": null
      },
      {
        "t": "2020-01-01T00:00:01Z",
        "spectral_entropy": null
      },
      {
        "t": "2020-01-01T00:00:02Z",
        "spectral_entropy": null
      },
      {
        "t": "2020-01-01T00:00:03Z",
        "spectral_entropy": null
      },
      {
        "t": "2020-01-01T00:00:04Z",
        "spectral_entropy": null
      },
      {
        "t": "2020-01-01T00:00:05Z",
        "spectral_entropy": null
      },
      {
        "t": "2020-01-01T00:00:06Z",
        "spectral_entropy": null
      },
      {
        "t": "2020-01-01T00:00:07Z",
        "spectral_entropy": null
      },
      {
        "t": "2020-01-01T00:00:08Z",
        "spectral_entropy": null
      },
      {
        "t": "2020-01-01T00:00:09Z",
        "spectral_entropy": null
      },
      {
        "t": "2020-01-01T00:00:10Z",
        "spectral_entropy": 0.7828
      },
      {
        "t": "2020-01-01T00:00:11Z",
        "spectral_entropy": 0.8756
      },
      {
        "t": "2020-01-01T00:00:12Z",
        "spectral_entropy": 0.8147
      },
      {
        "t": "2020-01-01T00:00:13Z",
        "spectral_entropy": 0.8491
      },
      {
        "t": "2020-01-01T00:00:14Z",
        "spectral_entropy": 0.767
      },
      {
        "t": "2020-01-01T00:00:15Z",
        "spectral_entropy": 0.909
      },
      {
        "t": "2020-01-01T00:00:16Z",
        "spectral_entropy": 0.8555
      },
      {
        "t": "2020-01-01T00:00:17Z",
        "spectral_entropy": 0.8196
      },
      {
        "t": "2020-01-01T00:00:18Z",
        "spectral_entropy": 0.8916
      },
      {
        "t": "2020-01-01T00:00:19Z",
        "spectral_entropy": 0.7759
      },
      {
        "t": "2020-01-01T00:00:20Z",
        "spectral_entropy": 0.8338
      },
      {
        "t": "2020-01-01T00:00:21Z",
        "spectral_entropy": 0.6311
      },
      {
        "t": "2020-01-01T00:00:22Z",
        "spectral_entropy": 0.6767
      },
      {
        "t": "2020-01-01T00:00:23Z",
        "spectral_entropy": 0.6758
      },
      {
        "t": "2020-01-01T00:00:24Z",
        "spectral_entropy": 0.6717
      },
      {
        "t": "2020-01-01T00:00:25Z",
        "spectral_entropy": 0.6948
      },
      {
        "t": "2020-01-01T00:00:26Z",
        "spectral_entropy": 0.5559
      },
      {
        "t": "2020-01-01T00:00:27Z",
        "spectral_entropy": 0.6497
      },
      {
        "t": "2020-01-01T00:00:28Z",
        "spectral_entropy": 0.5727
      },
      {
        "t": "2020-01-01T00:00:29Z",
        "spectral_entropy": 0.43
      },
      {
        "t": "2020-01-01T00:00:30Z",
        "spectral_entropy": 0.6639
      },
      {
        "t": "2020-01-01T00:00:31Z",
        "spectral_entropy": 0.7041
      },
      {
        "t": "2020-01-01T00:00:32Z",
        "spectral_entropy": 0.8487
      },
      {
        "t": "2020-01-01T00:00:33Z",
        "spectral_entropy": 0.9674
      },
      {
        "t": "2020-01-01T00:00:34Z",
        "spectral_entropy": 0.9497
      },
      {
        "t": "2020-01-01T00:00:35Z",
        "spectral_entropy": 0.8717
      },
      {
        "t": "2020-01-01T00:00:36Z",
        "spectral_entropy": 0.7976
      },
      {
        "t": "2020-01-01T00:00:37Z",
        "spectral_entropy": 0.9335
      },
      {
        "t": "2020-01-01T00:00:38Z",
        "spectral_entropy": 0.9169
      },
      {
        "t": "2020-01-01T00:00:39Z",
        "spectral_entropy": 0.9019
      },
      {
        "t": "2020-01-01T00:00:40Z",
        "spectral_entropy": 0.8931
      },
      {
        "t": "2020-01-01T00:00:41Z",
        "spectral_entropy": 0.8944
      },
      {
        "t": "2020-01-01T00:00:42Z",
        "spectral_entropy": 0.8931
      },
      {
        "t": "2020-01-01T00:00:43Z",
        "spectral_entropy": 0.5813
      },
      {
        "t": "2020-01-01T00:00:44Z",
        "spectral_entropy": 0.5119
      },
      {
        "t": "2020-01-01T00:00:45Z",
        "spectral_entropy": 0.7879
      },
      {
        "t": "2020-01-01T00:00:46Z",
        "spectral_entropy": 0.8048
      },
      {
        "t": "2020-01-01T00:00:47Z",
        "spectral_entropy": 0.9073
      },
      {
        "t": "2020-01-01T00:00:48Z",
        "spectral_entropy": 0.9107
      },
      {
        "t": "2020-01-01T00:00:49Z",
        "spectral_entropy": 0.702
      },
      {
        "t": "2020-01-01T00:00:50Z",
        "spectral_entropy": 0.8287
      },
      {
        "t": "2020-01-01T00:00:51Z",
        "spectral_entropy": 0.9029
      },
      {
        "t": "2020-01-01T00:00:52Z",
        "spectral_entropy": 0.9058
      },
      {
        "t": "2020-01-01T00:00:53Z",
        "spectral_entropy": 0.8519
      },
      {
        "t": "2020-01-01T00:00:54Z",
        "spectral_entropy": 0.8182
      },
      {
        "t": "2020-01-01T00:00:55Z",
        "spectral_entropy": 0.7669
      },
      {
        "t": "2020-01-01T00:00:56Z",
        "spectral_entropy": 0.736
      },
      {
        "t": "2020-01-01T00:00:57Z",
        "spectral_entropy": 0.7947
      },
      {
        "t": "2020-01-01T00:00:58Z",
        "spectral_entropy": 0.9178
      },
      {
        "t": "2020-01-01T00:00:59Z",
        "spectral_entropy": 0.9672
      },
      {
        "t": "2020-01-01T00:01:00Z",
        "spectral_entropy": 0.7465
      },
      {
        "t": "2020-01-01T00:01:01Z",
        "spectral_entropy": 0.794
      },
      {
        "t": "2020-01-01T00:01:02Z",
        "spectral_entropy": 0.8563
      },
      {
        "t": "2020-01-01T00:01:03Z",
        "spectral_entropy": 0.7747
      },
      {
        "t": "2020-01-01T00:01:04Z",
        "spectral_entropy": 0.7304
      },
      {
        "t": "2020-01-01T00:01:05Z",
        "spectral_entropy": 0.7132
      },
      {
        "t": "2020-01-01T00:01:06Z",
        "spectral_entropy": 0.7164
      },
      {
        "t": "2020-01-01T00:01:07Z",
        "spectral_entropy": 0.5837
      },
      {
        "t": "2020-01-01T00:01:08Z",
        "spectral_entropy": 0.5777
      },
      {
        "t": "2020-01-01T00:01:09Z",
        "spectral_entropy": 0.5541
      },
      {
        "t": "2020-01-01T00:01:10Z",
        "spectral_entropy": 0.5569
      },
      {
        "t": "2020-01-01T00:01:11Z",
        "spectral_entropy": 0.6078
      },
      {
        "t": "2020-01-01T00:01:12Z",
        "spectral_entropy": 0.6105
      },
      {
        "t": "2020-01-01T00:01:13Z",
        "spectral_entropy": 0.8269
      },
      {
        "t": "2020-01-01T00:01:14Z",
        "spectral_entropy": 0.7169
      },
      {
        "t": "2020-01-01T00:01:15Z",
        "spectral_entropy": 0.7165
      },
      {
        "t": "2020-01-01T00:01:16Z",
        "spectral_entropy": 0.7458
      },
      {
        "t": "2020-01-01T00:01:17Z",
        "spectral_entropy": 0.7422
      },
      {
        "t": "2020-01-01T00:01:18Z",
        "spectral_entropy": 0.7609
      },
      {
        "t": "2020-01-01T00:01:19Z",
        "spectral_entropy": 0.7731
      },
      {
        "t": "2020-01-01T00:01:20Z",
        "spectral_entropy": 0.8091
      },
      {
        "t": "2020-01-01T00:01:21Z",
        "spectral_entropy": 0.8663
      },
      {
        "t": "2020-01-01T00:01:22Z",
        "spectral_entropy": 0.8425
      },
      {
        "t": "2020-01-01T00:01:23Z",
        "spectral_entropy": 0.7117
      },
      {
        "t": "2020-01-01T00:01:24Z",
        "spectral_entropy": 0.6854
      },
      {
        "t": "2020-01-01T00:01:25Z",
        "spectral_entropy": 0.6605
      },
      {
        "t": "2020-01-01T00:01:26Z",
        "spectral_entropy": 0.6523
      },
      {
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