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.

Date and time 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

Data assumptions

All current endpoints assume that the time series data is equidistant (evenly spaced in time).

Timeout

All endpoints terminate after 60 seconds.

Authentication

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

To generate an API key, sign up for an account.

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.
402 Payment Required The parameters were valid, but the account requires billing information to continue making API requests.
404 Not Found The requested resource or route does not exist.
500 Internal Server Error Something went wrong on our side.

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.

Endpoints that make certain data assumptions, provide (automatic) data transformations prior to the main analysis to deliver valid results.

Transparency

Each response contains the applied arguments, every imputed missing value and every data transformation – enabling full reproducibility of the results.

Time series data

if missing values

Missing value imputation

if data assumptions

Data transformation

Statistical computation

f(x)

Result

Applied arguments

if missing values

Imputed values

if data assumptions

Applied data transformations

Statistical computation results

collective and point anomalies

POST /invocation/collective-and-point-anomalies

Anomaly detection
univariate | parametric

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

ARGUMENTS

data
REQUIREDarraydatasets: 1min data points: 100max data points: 10000

The time series data. An object in data represents 1 distinct time series. Keys must be encoded according to the ISO8601 date and time format subset RFC 3339, section 5.6. The value of existing data points must be a number, the value of missing data points must be encoded as null.

imputation
optionalstringdefault: linear
valid values: linear, spline, stineman, mean, median, mode, locf, nocb, sma, lwma, ewma, kalman

Imputation of missing values. Argument ignored if no missing values exist.

transformation
optionalobject

Performs (automatic) transformations of the time series data prior to the main analysis to fulfill parametric model assumptions.

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_collective_anomaly_size
optionalintegerdefault: 10min: 2

The minimum size of collective anomalies in number of data points to be considered as such. Changed to floor(time series length / 2), if larger than time series length / 2.

precision
optionalobject

Decimal point precision of the output data.

RETURNS

report.computation_time

The actual and billed computation time of the invocation in milliseconds.

result.arguments

The applied arguments.

In rare cases, the applied arguments can deviate from the arguments of the request. To make this fully transparent, the applied arguments are returned with each response.

For example, result.arguments.imputation is returned as null, if no missing values exist in the time series data of the request, to indicate that no imputation was applied.

result.imputation

The imputed missing values and the corresponding time indices.

result.transformation

The performed data transformations.

If a transformation was not applied, it is returned as null in result.transformation.

For example, if the arguments period and seasonal_differences of the request are both auto and are both returned as null in result.transformation, this implies that no dominant frequency has been found to determine the period and thus no seasonal differencing has been applied.

result.data

The output of the statistical computation.

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

If first_differences + seasonal_differences * period (in result.transformation) > 0, result.data starts with initial null values of the corresponding length.

{
  "data": [
    {
      "2020-01-01T00:00:00Z": 1.0137,
      "2020-01-01T00:00:01Z": 0.8591,
      "2020-01-01T00:00:02Z": 0.6281,
      "2020-01-01T00:00:03Z": 0.0703,
      "2020-01-01T00:00:04Z": -1.2546,
      "2020-01-01T00:00:05Z": 0.0635,
      "2020-01-01T00:00:06Z": 0.9731,
      "2020-01-01T00:00:07Z": 1.1618,
      "2020-01-01T00:00:08Z": 2.5978,
      "2020-01-01T00:00:09Z": 3.9978,
      "2020-01-01T00:00:10Z": 4.0237,
      "2020-01-01T00:00:11Z": 4.6535,
      "2020-01-01T00:00:12Z": 5.0346,
      "2020-01-01T00:00:13Z": 4.8492,
      "2020-01-01T00:00:14Z": 5.3419,
      "2020-01-01T00:00:15Z": 5.0351,
      "2020-01-01T00:00:16Z": 3.7687,
      "2020-01-01T00:00:17Z": 3.374,
      "2020-01-01T00:00:18Z": 1.1942,
      "2020-01-01T00:00:19Z": -1.0547,
      "2020-01-01T00:00:20Z": -3.3157,
      "2020-01-01T00:00:21Z": -5.057,
      "2020-01-01T00:00:22Z": -6.691,
      "2020-01-01T00:00:23Z": -7.6573,
      "2020-01-01T00:00:24Z": -7.6522,
      "2020-01-01T00:00:25Z": -7.2028,
      "2020-01-01T00:00:26Z": -5.7701,
      "2020-01-01T00:00:27Z": -4.5187,
      "2020-01-01T00:00:28Z": -3.7872,
      "2020-01-01T00:00:29Z": -4.2919,
      "2020-01-01T00:00:30Z": -3.8214,
      "2020-01-01T00:00:31Z": -4.195,
      "2020-01-01T00:00:32Z": -3.5719,
      "2020-01-01T00:00:33Z": -2.4975,
      "2020-01-01T00:00:34Z": -2.787,
      "2020-01-01T00:00:35Z": -3.6928,
      "2020-01-01T00:00:36Z": -3.2771,
      "2020-01-01T00:00:37Z": -3.8647,
      "2020-01-01T00:00:38Z": -2.9803,
      "2020-01-01T00:00:39Z": -3.6646,
      "2020-01-01T00:00:40Z": -2.829,
      "2020-01-01T00:00:41Z": -3.1812,
      "2020-01-01T00:00:42Z": -2.3828,
      "2020-01-01T00:00:43Z": -2.7223,
      "2020-01-01T00:00:44Z": -2.7717,
      "2020-01-01T00:00:45Z": -1.8045,
      "2020-01-01T00:00:46Z": -0.5042,
      "2020-01-01T00:00:47Z": 1.3069,
      "2020-01-01T00:00:48Z": 2.7687,
      "2020-01-01T00:00:49Z": 3.9865,
      "2020-01-01T00:00:50Z": 2.7695,
      "2020-01-01T00:00:51Z": 3.1204,
      "2020-01-01T00:00:52Z": 4.742,
      "2020-01-01T00:00:53Z": 7.6089,
      "2020-01-01T00:00:54Z": 9.054,
      "2020-01-01T00:00:55Z": 9.3756,
      "2020-01-01T00:00:56Z": 10.36,
      "2020-01-01T00:00:57Z": 11.1193,
      "2020-01-01T00:00:58Z": 11.5563,
      "2020-01-01T00:00:59Z": 13.6662,
      "2020-01-01T00:01:00Z": 15.6862,
      "2020-01-01T00:01:01Z": 18.0665,
      "2020-01-01T00:01:02Z": 19.3616,
      "2020-01-01T00:01:03Z": 19.8506,
      "2020-01-01T00:01:04Z": 20.7675,
      "2020-01-01T00:01:05Z": 20.6054,
      "2020-01-01T00:01:06Z": 19.2565,
      "2020-01-01T00:01:07Z": 18.536,
      "2020-01-01T00:01:08Z": 19.3415,
      "2020-01-01T00:01:09Z": 21.0423,
      "2020-01-01T00:01:10Z": 23.8812,
      "2020-01-01T00:01:11Z": 25.6965,
      "2020-01-01T00:01:12Z": 27.7823,
      "2020-01-01T00:01:13Z": 26.512,
      "2020-01-01T00:01:14Z": 26.2565,
      "2020-01-01T00:01:15Z": 26.0911,
      "2020-01-01T00:01:16Z": 25.4152,
      "2020-01-01T00:01:17Z": 24.8234,
      "2020-01-01T00:01:18Z": 23.2512,
      "2020-01-01T00:01:19Z": 24.0036,
      "2020-01-01T00:01:20Z": 24.9257,
      "2020-01-01T00:01:21Z": 25.5759,
      "2020-01-01T00:01:22Z": 27.1171,
      "2020-01-01T00:01:23Z": 28.4398,
      "2020-01-01T00:01:24Z": 28.5233,
      "2020-01-01T00:01:25Z": 26.8893,
      "2020-01-01T00:01:26Z": 25.8306,
      "2020-01-01T00:01:27Z": 25.2715,
      "2020-01-01T00:01:28Z": 24.0688,
      "2020-01-01T00:01:29Z": 24.6046,
      "2020-01-01T00:01:30Z": 24.6625,
      "2020-01-01T00:01:31Z": 24.1545,
      "2020-01-01T00:01:32Z": 23.4331,
      "2020-01-01T00:01:33Z": 22.8225,
      "2020-01-01T00:01:34Z": 20.5345,
      "2020-01-01T00:01:35Z": 21.5842,
      "2020-01-01T00:01:36Z": 22.3886,
      "2020-01-01T00:01:37Z": 23.4767,
      "2020-01-01T00:01:38Z": 22.5141,
      "2020-01-01T00:01:39Z": 23.3534
    }
  ],
  "imputation": "linear",
  "transformation": {
    "period": "auto",
    "box_cox_lambda": "auto",
    "seasonal_differences": "auto",
    "first_differences": "auto"
  },
  "method": "mean_var",
  "min_collective_anomaly_size": 10,
  "precision": {
    "digits": 4,
    "method": "significant"
  }
}
{
  "report": {
    "computation_time": {
      "actual": 1068.39,
      "billed": 1100
    }
  },
  "result": {
    "arguments": {
      "imputation": null,
      "transformation": {
        "period": "auto",
        "box_cox_lambda": "auto",
        "seasonal_differences": "auto",
        "first_differences": "auto"
      },
      "method": "mean_var",
      "min_collective_anomaly_size": 10,
      "precision": {
        "digits": 4,
        "method": "significant"
      }
    },
    "imputation": [],
    "transformation": {
      "period": null,
      "box_cox_lambda": 1.072,
      "seasonal_differences": null,
      "first_differences": 1
    },
    "data": {
      "collective_anomalies": [
        {
          "t": "2020-01-01T00:00:15Z",
          "mean_change_strength": 2.815,
          "variance_change_strength": 0.1819,
          "size": 10
        }
      ],
      "point_anomalies": []
    }
  }
}
{
  "report": {
    "computation_time": {
      "actual": 1068.39,
      "billed": 1100
    }
  },
  "result": {
    "arguments": {
      "imputation": null,
      "transformation": {
        "period": "auto",
        "box_cox_lambda": "auto",
        "seasonal_differences": "auto",
        "first_differences": "auto"
      },
      "method": "mean_var",
      "min_collective_anomaly_size": 10,
      "precision": {
        "digits": 4,
        "method": "significant"
      }
    },
    "imputation": [],
    "transformation": {
      "period": null,
      "box_cox_lambda": 1.072,
      "seasonal_differences": null,
      "first_differences": 1
    },
    "data": {
      "collective_anomalies": [
        {
          "t": "2020-01-01T00:00:15Z",
          "mean_change_strength": 2.815,
          "variance_change_strength": 0.1819,
          "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

data
REQUIREDarraydatasets: 1min data points: 10max data points: 10000

The time series data. An object in data represents 1 distinct time series. Keys must be encoded according to the ISO8601 date and time format subset RFC 3339, section 5.6. The value of existing data points must be a number, the value of missing data points must be encoded as null.

imputation
optionalstringdefault: linear
valid values: linear, spline, stineman, mean, median, mode, locf, nocb, sma, lwma, ewma, kalman

Imputation of missing values. Argument ignored if no missing values exist.

alpha
optionalnumberdefault: 0.05min: 0.01max: 0.2

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 floor(time series length / 2), if larger than time series length / 2.

precision
optionalobject

Decimal point precision of the output data.

RETURNS

report.computation_time

The actual and billed computation time of the invocation in milliseconds.

result.arguments

The applied arguments.

In rare cases, the applied arguments can deviate from the arguments of the request. To make this fully transparent, the applied arguments are returned with each response.

For example, result.arguments.imputation is returned as null, if no missing values exist in the time series data of the request, to indicate that no imputation was applied.

For example, the argument window_size is changed to floor(time series length / 2), if set to a value greater than time series length / 2.

result.imputation

The imputed missing values and the corresponding time indices.

result.data

The output of the statistical computation.

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

The initial null values in result.data correspond to the moving window. The length of this sequence is window_size (in result.arguments) - 1.

{
  "data": [
    {
      "2020-01-01T00:00:00Z": 1.0137,
      "2020-01-01T00:00:01Z": 0.8591,
      "2020-01-01T00:00:02Z": 0.6281,
      "2020-01-01T00:00:03Z": 0.0703,
      "2020-01-01T00:00:04Z": -1.2546,
      "2020-01-01T00:00:05Z": 0.0635,
      "2020-01-01T00:00:06Z": 0.9731,
      "2020-01-01T00:00:07Z": 1.1618,
      "2020-01-01T00:00:08Z": 2.5978,
      "2020-01-01T00:00:09Z": 3.9978,
      "2020-01-01T00:00:10Z": 4.0237,
      "2020-01-01T00:00:11Z": 4.6535,
      "2020-01-01T00:00:12Z": 5.0346,
      "2020-01-01T00:00:13Z": 4.8492,
      "2020-01-01T00:00:14Z": 5.3419,
      "2020-01-01T00:00:15Z": 5.0351,
      "2020-01-01T00:00:16Z": 3.7687,
      "2020-01-01T00:00:17Z": 3.374,
      "2020-01-01T00:00:18Z": 1.1942,
      "2020-01-01T00:00:19Z": -1.0547,
      "2020-01-01T00:00:20Z": -3.3157,
      "2020-01-01T00:00:21Z": -5.057,
      "2020-01-01T00:00:22Z": -6.691,
      "2020-01-01T00:00:23Z": -7.6573,
      "2020-01-01T00:00:24Z": -7.6522,
      "2020-01-01T00:00:25Z": -7.2028,
      "2020-01-01T00:00:26Z": -5.7701,
      "2020-01-01T00:00:27Z": -4.5187,
      "2020-01-01T00:00:28Z": -3.7872,
      "2020-01-01T00:00:29Z": -4.2919,
      "2020-01-01T00:00:30Z": -3.8214,
      "2020-01-01T00:00:31Z": -4.195,
      "2020-01-01T00:00:32Z": -3.5719,
      "2020-01-01T00:00:33Z": -2.4975,
      "2020-01-01T00:00:34Z": -2.787,
      "2020-01-01T00:00:35Z": -3.6928,
      "2020-01-01T00:00:36Z": -3.2771,
      "2020-01-01T00:00:37Z": -3.8647,
      "2020-01-01T00:00:38Z": -2.9803,
      "2020-01-01T00:00:39Z": -3.6646,
      "2020-01-01T00:00:40Z": -2.829,
      "2020-01-01T00:00:41Z": -3.1812,
      "2020-01-01T00:00:42Z": -2.3828,
      "2020-01-01T00:00:43Z": -2.7223,
      "2020-01-01T00:00:44Z": -2.7717,
      "2020-01-01T00:00:45Z": -1.8045,
      "2020-01-01T00:00:46Z": -0.5042,
      "2020-01-01T00:00:47Z": 1.3069,
      "2020-01-01T00:00:48Z": 2.7687,
      "2020-01-01T00:00:49Z": 3.9865,
      "2020-01-01T00:00:50Z": 2.7695,
      "2020-01-01T00:00:51Z": 3.1204,
      "2020-01-01T00:00:52Z": 4.742,
      "2020-01-01T00:00:53Z": 7.6089,
      "2020-01-01T00:00:54Z": 9.054,
      "2020-01-01T00:00:55Z": 9.3756,
      "2020-01-01T00:00:56Z": 10.36,
      "2020-01-01T00:00:57Z": 11.1193,
      "2020-01-01T00:00:58Z": 11.5563,
      "2020-01-01T00:00:59Z": 13.6662,
      "2020-01-01T00:01:00Z": 15.6862,
      "2020-01-01T00:01:01Z": 18.0665,
      "2020-01-01T00:01:02Z": 19.3616,
      "2020-01-01T00:01:03Z": 19.8506,
      "2020-01-01T00:01:04Z": 20.7675,
      "2020-01-01T00:01:05Z": 20.6054,
      "2020-01-01T00:01:06Z": 19.2565,
      "2020-01-01T00:01:07Z": 18.536,
      "2020-01-01T00:01:08Z": 19.3415,
      "2020-01-01T00:01:09Z": 21.0423,
      "2020-01-01T00:01:10Z": 23.8812,
      "2020-01-01T00:01:11Z": 25.6965,
      "2020-01-01T00:01:12Z": 27.7823,
      "2020-01-01T00:01:13Z": 26.512,
      "2020-01-01T00:01:14Z": 26.2565,
      "2020-01-01T00:01:15Z": 26.0911,
      "2020-01-01T00:01:16Z": 25.4152,
      "2020-01-01T00:01:17Z": 24.8234,
      "2020-01-01T00:01:18Z": 23.2512,
      "2020-01-01T00:01:19Z": 24.0036,
      "2020-01-01T00:01:20Z": 24.9257,
      "2020-01-01T00:01:21Z": 25.5759,
      "2020-01-01T00:01:22Z": 27.1171,
      "2020-01-01T00:01:23Z": 28.4398,
      "2020-01-01T00:01:24Z": 28.5233,
      "2020-01-01T00:01:25Z": 26.8893,
      "2020-01-01T00:01:26Z": 25.8306,
      "2020-01-01T00:01:27Z": 25.2715,
      "2020-01-01T00:01:28Z": 24.0688,
      "2020-01-01T00:01:29Z": 24.6046,
      "2020-01-01T00:01:30Z": 24.6625,
      "2020-01-01T00:01:31Z": 24.1545,
      "2020-01-01T00:01:32Z": 23.4331,
      "2020-01-01T00:01:33Z": 22.8225,
      "2020-01-01T00:01:34Z": 20.5345,
      "2020-01-01T00:01:35Z": 21.5842,
      "2020-01-01T00:01:36Z": 22.3886,
      "2020-01-01T00:01:37Z": 23.4767,
      "2020-01-01T00:01:38Z": 22.5141,
      "2020-01-01T00:01:39Z": 23.3534
    }
  ],
  "imputation": "linear",
  "alpha": 0.05,
  "window_size": 10,
  "precision": {
    "digits": 4,
    "method": "significant"
  }
}
{
  "report": {
    "computation_time": {
      "actual": 514.87,
      "billed": 600
    }
  },
  "result": {
    "arguments": {
      "imputation": null,
      "alpha": 0.05,
      "window_size": 10,
      "precision": {
        "digits": 4,
        "method": "significant"
      }
    },
    "imputation": [],
    "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
      },
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    ]
  }
}
        

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

data
REQUIREDarraydatasets: 1min data points: 100max data points: 10000

The time series data. An object in data represents 1 distinct time series. Keys must be encoded according to the ISO8601 date and time format subset RFC 3339, section 5.6. The value of existing data points must be a number, the value of missing data points must be encoded as null.

imputation
optionalstringdefault: linear
valid values: linear, spline, stineman, mean, median, mode, locf, nocb, sma, lwma, ewma, kalman

Imputation of missing values. Argument ignored if no missing values exist.

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.

precision
optionalobject

Decimal point precision of the output data.

RETURNS

report.computation_time

The actual and billed computation time of the invocation in milliseconds.

result.arguments

The applied arguments.

In rare cases, the applied arguments can deviate from the arguments of the request. To make this fully transparent, the applied arguments are returned with each response.

For example, result.arguments.imputation is returned as null, if no missing values exist in the time series data of the request, to indicate that no imputation was applied.

result.imputation

The imputed missing values and the corresponding time indices.

result.data

The output of the statistical computation.

// Tokenization skipped
{
  "data": [
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}
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          "x": 27.94,
          "drift": 0.09189,
          "diffusion": 0,
          "jump": 1.46,
          "total_variance": 1.387,
          "conditional_variance": 9.249
        },
        {
          "x": 28.02,
          "drift": 0.09013,
          "diffusion": 0,
          "jump": 1.457,
          "total_variance": 1.386,
          "conditional_variance": 9.181
        },
        {
          "x": 28.09,
          "drift": 0.08839,
          "diffusion": 0,
          "jump": 1.454,
          "total_variance": 1.385,
          "conditional_variance": 9.113
        },
        {
          "x": 28.16,
          "drift": 0.08665,
          "diffusion": 0,
          "jump": 1.451,
          "total_variance": 1.384,
          "conditional_variance": 9.047
        },
        {
          "x": 28.23,
          "drift": 0.08492,
          "diffusion": 0,
          "jump": 1.449,
          "total_variance": 1.383,
          "conditional_variance": 8.982
        },
        {
          "x": 28.31,
          "drift": 0.08319,
          "diffusion": 0,
          "jump": 1.446,
          "total_variance": 1.382,
          "conditional_variance": 8.918
        },
        {
          "x": 28.38,
          "drift": 0.08147,
          "diffusion": 0,
          "jump": 1.443,
          "total_variance": 1.38,
          "conditional_variance": 8.855
        },
        {
          "x": 28.45,
          "drift": 0.07976,
          "diffusion": 0,
          "jump": 1.44,
          "total_variance": 1.379,
          "conditional_variance": 8.793
        },
        {
          "x": 28.52,
          "drift": 0.07806,
          "diffusion": 0,
          "jump": 1.437,
          "total_variance": 1.378,
          "conditional_variance": 8.732
        }
      ]
    }
  }
}
        

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

data
REQUIREDarraydatasets: 1min data points: 10max data points: 10000

The time series data. An object in data represents 1 distinct time series. Keys must be encoded according to the ISO8601 date and time format subset RFC 3339, section 5.6. The value of existing data points must be a number, the value of missing data points must be encoded as null.

imputation
optionalstringdefault: linear
valid values: linear, spline, stineman, mean, median, mode, locf, nocb, sma, lwma, ewma, kalman

Imputation of missing values. Argument ignored if no missing values exist.

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.

window_size
optionalintegerdefault: 10min: 5

The size of the moving window in number of data points. Changed to floor(time series length / 2), if larger than time series length / 2.

exclusion_factor
optionalnumberdefault: 0.5min: 0max: 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.

precision
optionalobject

Decimal point precision of the output data.

RETURNS

report.computation_time

The actual and billed computation time of the invocation in milliseconds.

result.arguments

The applied arguments.

In rare cases, the applied arguments can deviate from the arguments of the request. To make this fully transparent, the applied arguments are returned with each response.

For example, result.arguments.imputation is returned as null, if no missing values exist in the time series data of the request, to indicate that no imputation was applied.

For example, the argument window_size is changed to floor(time series length / 2), if set to a value greater than time series length / 2.

result.imputation

The imputed missing values and the corresponding time indices.

result.data

The output of the statistical computation.

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

The final null values in result.data correspond to the moving window. The length of this sequence is window_size (in result.arguments) - 1.

{
  "data": [
    {
      "2020-01-01T00:00:00Z": 1.0137,
      "2020-01-01T00:00:01Z": 0.8591,
      "2020-01-01T00:00:02Z": 0.6281,
      "2020-01-01T00:00:03Z": 0.0703,
      "2020-01-01T00:00:04Z": -1.2546,
      "2020-01-01T00:00:05Z": 0.0635,
      "2020-01-01T00:00:06Z": 0.9731,
      "2020-01-01T00:00:07Z": 1.1618,
      "2020-01-01T00:00:08Z": 2.5978,
      "2020-01-01T00:00:09Z": 3.9978,
      "2020-01-01T00:00:10Z": 4.0237,
      "2020-01-01T00:00:11Z": 4.6535,
      "2020-01-01T00:00:12Z": 5.0346,
      "2020-01-01T00:00:13Z": 4.8492,
      "2020-01-01T00:00:14Z": 5.3419,
      "2020-01-01T00:00:15Z": 5.0351,
      "2020-01-01T00:00:16Z": 3.7687,
      "2020-01-01T00:00:17Z": 3.374,
      "2020-01-01T00:00:18Z": 1.1942,
      "2020-01-01T00:00:19Z": -1.0547,
      "2020-01-01T00:00:20Z": -3.3157,
      "2020-01-01T00:00:21Z": -5.057,
      "2020-01-01T00:00:22Z": -6.691,
      "2020-01-01T00:00:23Z": -7.6573,
      "2020-01-01T00:00:24Z": -7.6522,
      "2020-01-01T00:00:25Z": -7.2028,
      "2020-01-01T00:00:26Z": -5.7701,
      "2020-01-01T00:00:27Z": -4.5187,
      "2020-01-01T00:00:28Z": -3.7872,
      "2020-01-01T00:00:29Z": -4.2919,
      "2020-01-01T00:00:30Z": -3.8214,
      "2020-01-01T00:00:31Z": -4.195,
      "2020-01-01T00:00:32Z": -3.5719,
      "2020-01-01T00:00:33Z": -2.4975,
      "2020-01-01T00:00:34Z": -2.787,
      "2020-01-01T00:00:35Z": -3.6928,
      "2020-01-01T00:00:36Z": -3.2771,
      "2020-01-01T00:00:37Z": -3.8647,
      "2020-01-01T00:00:38Z": -2.9803,
      "2020-01-01T00:00:39Z": -3.6646,
      "2020-01-01T00:00:40Z": -2.829,
      "2020-01-01T00:00:41Z": -3.1812,
      "2020-01-01T00:00:42Z": -2.3828,
      "2020-01-01T00:00:43Z": -2.7223,
      "2020-01-01T00:00:44Z": -2.7717,
      "2020-01-01T00:00:45Z": -1.8045,
      "2020-01-01T00:00:46Z": -0.5042,
      "2020-01-01T00:00:47Z": 1.3069,
      "2020-01-01T00:00:48Z": 2.7687,
      "2020-01-01T00:00:49Z": 3.9865,
      "2020-01-01T00:00:50Z": 2.7695,
      "2020-01-01T00:00:51Z": 3.1204,
      "2020-01-01T00:00:52Z": 4.742,
      "2020-01-01T00:00:53Z": 7.6089,
      "2020-01-01T00:00:54Z": 9.054,
      "2020-01-01T00:00:55Z": 9.3756,
      "2020-01-01T00:00:56Z": 10.36,
      "2020-01-01T00:00:57Z": 11.1193,
      "2020-01-01T00:00:58Z": 11.5563,
      "2020-01-01T00:00:59Z": 13.6662,
      "2020-01-01T00:01:00Z": 15.6862,
      "2020-01-01T00:01:01Z": 18.0665,
      "2020-01-01T00:01:02Z": 19.3616,
      "2020-01-01T00:01:03Z": 19.8506,
      "2020-01-01T00:01:04Z": 20.7675,
      "2020-01-01T00:01:05Z": 20.6054,
      "2020-01-01T00:01:06Z": 19.2565,
      "2020-01-01T00:01:07Z": 18.536,
      "2020-01-01T00:01:08Z": 19.3415,
      "2020-01-01T00:01:09Z": 21.0423,
      "2020-01-01T00:01:10Z": 23.8812,
      "2020-01-01T00:01:11Z": 25.6965,
      "2020-01-01T00:01:12Z": 27.7823,
      "2020-01-01T00:01:13Z": 26.512,
      "2020-01-01T00:01:14Z": 26.2565,
      "2020-01-01T00:01:15Z": 26.0911,
      "2020-01-01T00:01:16Z": 25.4152,
      "2020-01-01T00:01:17Z": 24.8234,
      "2020-01-01T00:01:18Z": 23.2512,
      "2020-01-01T00:01:19Z": 24.0036,
      "2020-01-01T00:01:20Z": 24.9257,
      "2020-01-01T00:01:21Z": 25.5759,
      "2020-01-01T00:01:22Z": 27.1171,
      "2020-01-01T00:01:23Z": 28.4398,
      "2020-01-01T00:01:24Z": 28.5233,
      "2020-01-01T00:01:25Z": 26.8893,
      "2020-01-01T00:01:26Z": 25.8306,
      "2020-01-01T00:01:27Z": 25.2715,
      "2020-01-01T00:01:28Z": 24.0688,
      "2020-01-01T00:01:29Z": 24.6046,
      "2020-01-01T00:01:30Z": 24.6625,
      "2020-01-01T00:01:31Z": 24.1545,
      "2020-01-01T00:01:32Z": 23.4331,
      "2020-01-01T00:01:33Z": 22.8225,
      "2020-01-01T00:01:34Z": 20.5345,
      "2020-01-01T00:01:35Z": 21.5842,
      "2020-01-01T00:01:36Z": 22.3886,
      "2020-01-01T00:01:37Z": 23.4767,
      "2020-01-01T00:01:38Z": 22.5141,
      "2020-01-01T00:01:39Z": 23.3534
    }
  ],
  "imputation": "linear",
  "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,
  "precision": {
    "digits": 4,
    "method": "significant"
  }
}
{
  "report": {
    "computation_time": {
      "actual": 358.58,
      "billed": 400
    }
  },
  "result": {
    "arguments": {
      "imputation": null,
      "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,
      "precision": {
        "digits": 4,
        "method": "significant"
      }
    },
    "imputation": [],
    "data": {
      "matrix_profile": [
        {
          "t": "2020-01-01T00:00:00Z",
          "distance": 0.9539
        },
        {
          "t": "2020-01-01T00:00:01Z",
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        },
        {
          "t": "2020-01-01T00:00:02Z",
          "distance": 1.028
        },
        {
          "t": "2020-01-01T00:00:03Z",
          "distance": 0.732
        },
        {
          "t": "2020-01-01T00:00:04Z",
          "distance": 0.5966
        },
        {
          "t": "2020-01-01T00:00:05Z",
          "distance": 0.622
        },
        {
          "t": "2020-01-01T00:00:06Z",
          "distance": 0.7389
        },
        {
          "t": "2020-01-01T00:00:07Z",
          "distance": 1.02
        },
        {
          "t": "2020-01-01T00:00:08Z",
          "distance": 1.713
        },
        {
          "t": "2020-01-01T00:00:09Z",
          "distance": 2.306
        },
        {
          "t": "2020-01-01T00:00:10Z",
          "distance": 1.92
        },
        {
          "t": "2020-01-01T00:00:11Z",
          "distance": 1.463
        },
        {
          "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
        },
        {
          "t": "2020-01-01T00:00:15Z",
          "distance": 1.213
        },
        {
          "t": "2020-01-01T00:00:16Z",
          "distance": 0.9444
        },
        {
          "t": "2020-01-01T00:00:17Z",
          "distance": 1.1
        },
        {
          "t": "2020-01-01T00:00:18Z",
          "distance": 1.429
        },
        {
          "t": "2020-01-01T00:00:19Z",
          "distance": 1.738
        },
        {
          "t": "2020-01-01T00:00:20Z",
          "distance": 1.791
        },
        {
          "t": "2020-01-01T00:00:21Z",
          "distance": 1.3
        },
        {
          "t": "2020-01-01T00:00:22Z",
          "distance": 0.7819
        },
        {
          "t": "2020-01-01T00:00:23Z",
          "distance": 0.6831
        },
        {
          "t": "2020-01-01T00:00:24Z",
          "distance": 0.8584
        },
        {
          "t": "2020-01-01T00:00:25Z",
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        },
        {
          "t": "2020-01-01T00:00:26Z",
          "distance": 1.667
        },
        {
          "t": "2020-01-01T00:00:27Z",
          "distance": 1.983
        },
        {
          "t": "2020-01-01T00:00:28Z",
          "distance": 2.029
        },
        {
          "t": "2020-01-01T00:00:29Z",
          "distance": 2.266
        },
        {
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        },
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          "t": "2020-01-01T00:00:31Z",
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        },
        {
          "t": "2020-01-01T00:00:32Z",
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        },
        {
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        {
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        {
          "t": "2020-01-01T00:00:52Z",
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        {
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        {
          "t": "2020-01-01T00:00:54Z",
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        },
        {
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          "distance": 0.6116
        },
        {
          "t": "2020-01-01T00:00:56Z",
          "distance": 0.5966
        },
        {
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        },
        {
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        {
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        {
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        {
          "t": "2020-01-01T00:01:09Z",
          "distance": 1.713
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        {
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        {
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        {
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          "distance": 0.9539
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        {
          "t": "2020-01-01T00:01:15Z",
          "distance": 0.689
        },
        {
          "t": "2020-01-01T00:01:16Z",
          "distance": 1.041
        },
        {
          "t": "2020-01-01T00:01:17Z",
          "distance": 1.31
        },
        {
          "t": "2020-01-01T00:01:18Z",
          "distance": 1.487
        },
        {
          "t": "2020-01-01T00:01:19Z",
          "distance": 1.906
        },
        {
          "t": "2020-01-01T00:01:20Z",
          "distance": 1.831
        },
        {
          "t": "2020-01-01T00:01:21Z",
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        },
        {
          "t": "2020-01-01T00:01:22Z",
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        {
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        {
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        {
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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": [
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    }
  }
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        },
        {
          "t": "2020-01-01T00:01:30Z",
          "distance": 1.738
        },
        {
          "t": "2020-01-01T00:01:31Z",
          "distance": null
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        {
          "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
        },
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          "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": [
        "2020-01-01T00:00:42Z",
        "2020-01-01T00:01:05Z",
        "2020-01-01T00:01:16Z"
      ]
    }
  }
}
        

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

data
REQUIREDarraydatasets: 1min data points: 100max data points: 10000

The time series data. An object in data represents 1 distinct time series. Keys must be encoded according to the ISO8601 date and time format subset RFC 3339, section 5.6. The value of existing data points must be a number, the value of missing data points must be encoded as null.

imputation
optionalstringdefault: linear
valid values: linear, spline, stineman, mean, median, mode, locf, nocb, sma, lwma, ewma, kalman

Imputation of missing values. Argument ignored if no missing values exist.

transformation
optionalobject

Performs (automatic) transformations of the time series data prior to the main analysis to fulfill parametric model assumptions.

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.

alpha
optionalnumberdefault: 0.05min: 0.01max: 0.2

The statistical significance level of the test.

precision
optionalobject

Decimal point precision of the output data.

RETURNS

report.computation_time

The actual and billed computation time of the invocation in milliseconds.

result.arguments

The applied arguments.

In rare cases, the applied arguments can deviate from the arguments of the request. To make this fully transparent, the applied arguments are returned with each response.

For example, result.arguments.imputation is returned as null, if no missing values exist in the time series data of the request, to indicate that no imputation was applied.

result.imputation

The imputed missing values and the corresponding time indices.

result.transformation

The performed data transformations.

If a transformation was not applied, it is returned as null in result.transformation.

For example, if the arguments period and seasonal_differences of the request are both auto and are both returned as null in result.transformation, this implies that no dominant frequency has been found to determine the period and thus no seasonal differencing has been applied.

result.data

The output of the statistical computation.

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

{
  "data": [
    {
      "2020-01-01T00:00:00Z": 1.0137,
      "2020-01-01T00:00:01Z": 0.8591,
      "2020-01-01T00:00:02Z": 0.6281,
      "2020-01-01T00:00:03Z": 0.0703,
      "2020-01-01T00:00:04Z": -1.2546,
      "2020-01-01T00:00:05Z": 0.0635,
      "2020-01-01T00:00:06Z": 0.9731,
      "2020-01-01T00:00:07Z": 1.1618,
      "2020-01-01T00:00:08Z": 2.5978,
      "2020-01-01T00:00:09Z": 3.9978,
      "2020-01-01T00:00:10Z": 4.0237,
      "2020-01-01T00:00:11Z": 4.6535,
      "2020-01-01T00:00:12Z": 5.0346,
      "2020-01-01T00:00:13Z": 4.8492,
      "2020-01-01T00:00:14Z": 5.3419,
      "2020-01-01T00:00:15Z": 5.0351,
      "2020-01-01T00:00:16Z": 3.7687,
      "2020-01-01T00:00:17Z": 3.374,
      "2020-01-01T00:00:18Z": 1.1942,
      "2020-01-01T00:00:19Z": -1.0547,
      "2020-01-01T00:00:20Z": -3.3157,
      "2020-01-01T00:00:21Z": -5.057,
      "2020-01-01T00:00:22Z": -6.691,
      "2020-01-01T00:00:23Z": -7.6573,
      "2020-01-01T00:00:24Z": -7.6522,
      "2020-01-01T00:00:25Z": -7.2028,
      "2020-01-01T00:00:26Z": -5.7701,
      "2020-01-01T00:00:27Z": -4.5187,
      "2020-01-01T00:00:28Z": -3.7872,
      "2020-01-01T00:00:29Z": -4.2919,
      "2020-01-01T00:00:30Z": -3.8214,
      "2020-01-01T00:00:31Z": -4.195,
      "2020-01-01T00:00:32Z": -3.5719,
      "2020-01-01T00:00:33Z": -2.4975,
      "2020-01-01T00:00:34Z": -2.787,
      "2020-01-01T00:00:35Z": -3.6928,
      "2020-01-01T00:00:36Z": -3.2771,
      "2020-01-01T00:00:37Z": -3.8647,
      "2020-01-01T00:00:38Z": -2.9803,
      "2020-01-01T00:00:39Z": -3.6646,
      "2020-01-01T00:00:40Z": -2.829,
      "2020-01-01T00:00:41Z": -3.1812,
      "2020-01-01T00:00:42Z": -2.3828,
      "2020-01-01T00:00:43Z": -2.7223,
      "2020-01-01T00:00:44Z": -2.7717,
      "2020-01-01T00:00:45Z": -1.8045,
      "2020-01-01T00:00:46Z": -0.5042,
      "2020-01-01T00:00:47Z": 1.3069,
      "2020-01-01T00:00:48Z": 2.7687,
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      "2020-01-01T00:00:51Z": 3.1204,
      "2020-01-01T00:00:52Z": 4.742,
      "2020-01-01T00:00:53Z": 7.6089,
      "2020-01-01T00:00:54Z": 9.054,
      "2020-01-01T00:00:55Z": 9.3756,
      "2020-01-01T00:00:56Z": 10.36,
      "2020-01-01T00:00:57Z": 11.1193,
      "2020-01-01T00:00:58Z": 11.5563,
      "2020-01-01T00:00:59Z": 13.6662,
      "2020-01-01T00:01:00Z": 15.6862,
      "2020-01-01T00:01:01Z": 18.0665,
      "2020-01-01T00:01:02Z": 19.3616,
      "2020-01-01T00:01:03Z": 19.8506,
      "2020-01-01T00:01:04Z": 20.7675,
      "2020-01-01T00:01:05Z": 20.6054,
      "2020-01-01T00:01:06Z": 19.2565,
      "2020-01-01T00:01:07Z": 18.536,
      "2020-01-01T00:01:08Z": 19.3415,
      "2020-01-01T00:01:09Z": 21.0423,
      "2020-01-01T00:01:10Z": 23.8812,
      "2020-01-01T00:01:11Z": 25.6965,
      "2020-01-01T00:01:12Z": 27.7823,
      "2020-01-01T00:01:13Z": 26.512,
      "2020-01-01T00:01:14Z": 26.2565,
      "2020-01-01T00:01:15Z": 26.0911,
      "2020-01-01T00:01:16Z": 25.4152,
      "2020-01-01T00:01:17Z": 24.8234,
      "2020-01-01T00:01:18Z": 23.2512,
      "2020-01-01T00:01:19Z": 24.0036,
      "2020-01-01T00:01:20Z": 24.9257,
      "2020-01-01T00:01:21Z": 25.5759,
      "2020-01-01T00:01:22Z": 27.1171,
      "2020-01-01T00:01:23Z": 28.4398,
      "2020-01-01T00:01:24Z": 28.5233,
      "2020-01-01T00:01:25Z": 26.8893,
      "2020-01-01T00:01:26Z": 25.8306,
      "2020-01-01T00:01:27Z": 25.2715,
      "2020-01-01T00:01:28Z": 24.0688,
      "2020-01-01T00:01:29Z": 24.6046,
      "2020-01-01T00:01:30Z": 24.6625,
      "2020-01-01T00:01:31Z": 24.1545,
      "2020-01-01T00:01:32Z": 23.4331,
      "2020-01-01T00:01:33Z": 22.8225,
      "2020-01-01T00:01:34Z": 20.5345,
      "2020-01-01T00:01:35Z": 21.5842,
      "2020-01-01T00:01:36Z": 22.3886,
      "2020-01-01T00:01:37Z": 23.4767,
      "2020-01-01T00:01:38Z": 22.5141,
      "2020-01-01T00:01:39Z": 23.3534
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  ],
  "imputation": "linear",
  "transformation": {
    "period": "auto",
    "box_cox_lambda": "auto",
    "seasonal_differences": "auto",
    "first_differences": "auto"
  },
  "method": "acf",
  "alpha": 0.05,
  "precision": {
    "digits": 4,
    "method": "significant"
  }
}
{
  "report": {
    "computation_time": {
      "actual": 1018.14,
      "billed": 1100
    }
  },
  "result": {
    "arguments": {
      "imputation": null,
      "transformation": {
        "period": "auto",
        "box_cox_lambda": "auto",
        "seasonal_differences": "auto",
        "first_differences": "auto"
      },
      "method": "acf",
      "alpha": 0.05,
      "precision": {
        "digits": 4,
        "method": "significant"
      }
    },
    "imputation": [],
    "transformation": {
      "period": null,
      "box_cox_lambda": 1.072,
      "seasonal_differences": null,
      "first_differences": 1
    },
    "data": [
      {
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        "acf": 0.5189,
        "p_value": 2.433e-7,
        "critical_value": 0.197
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      {
        "lag": 2,
        "acf": 0.3284,
        "p_value": 0.001086,
        "critical_value": 0.197
      },
      {
        "lag": 3,
        "acf": 0.08836,
        "p_value": 0.3793,
        "critical_value": 0.197
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      {
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        "acf": -0.003167,
        "p_value": 0.9749,
        "critical_value": 0.197
      },
      {
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        "acf": -0.08561,
        "p_value": 0.3943,
        "critical_value": 0.197
      },
      {
        "lag": 6,
        "acf": 0.00142,
        "p_value": 0.9887,
        "critical_value": 0.197
      },
      {
        "lag": 7,
        "acf": 0.07288,
        "p_value": 0.4684,
        "critical_value": 0.197
      },
      {
        "lag": 8,
        "acf": 0.1069,
        "p_value": 0.2875,
        "critical_value": 0.197
      },
      {
        "lag": 9,
        "acf": 0.0913,
        "p_value": 0.3637,
        "critical_value": 0.197
      },
      {
        "lag": 10,
        "acf": 0.09913,
        "p_value": 0.324,
        "critical_value": 0.197
      },
      {
        "lag": 11,
        "acf": 0.09495,
        "p_value": 0.3448,
        "critical_value": 0.197
      },
      {
        "lag": 12,
        "acf": 0.09163,
        "p_value": 0.3619,
        "critical_value": 0.197
      },
      {
        "lag": 13,
        "acf": 0.04043,
        "p_value": 0.6875,
        "critical_value": 0.197
      },
      {
        "lag": 14,
        "acf": -0.04395,
        "p_value": 0.6619,
        "critical_value": 0.197
      },
      {
        "lag": 15,
        "acf": 0.02277,
        "p_value": 0.8208,
        "critical_value": 0.197
      },
      {
        "lag": 16,
        "acf": 0.04113,
        "p_value": 0.6823,
        "critical_value": 0.197
      },
      {
        "lag": 17,
        "acf": 0.005567,
        "p_value": 0.9558,
        "critical_value": 0.197
      },
      {
        "lag": 18,
        "acf": 0.04269,
        "p_value": 0.671,
        "critical_value": 0.197
      },
      {
        "lag": 19,
        "acf": 0.0949,
        "p_value": 0.345,
        "critical_value": 0.197
      }
    ]
  }
}
{
  "report": {
    "computation_time": {
      "actual": 1018.14,
      "billed": 1100
    }
  },
  "result": {
    "arguments": {
      "imputation": null,
      "transformation": {
        "period": "auto",
        "box_cox_lambda": "auto",
        "seasonal_differences": "auto",
        "first_differences": "auto"
      },
      "method": "acf",
      "alpha": 0.05,
      "precision": {
        "digits": 4,
        "method": "significant"
      }
    },
    "imputation": [],
    "transformation": {
      "period": null,
      "box_cox_lambda": 1.072,
      "seasonal_differences": null,
      "first_differences": 1
    },
    "data": [
      {
        "lag": 1,
        "acf": 0.5189,
        "p_value": 2.433e-7,
        "critical_value": 0.197
      },
      {
        "lag": 2,
        "acf": 0.3284,
        "p_value": 0.001086,
        "critical_value": 0.197
      },
      {
        "lag": 3,
        "acf": 0.08836,
        "p_value": 0.3793,
        "critical_value": 0.197
      },
      {
        "lag": 4,
        "acf": -0.003167,
        "p_value": 0.9749,
        "critical_value": 0.197
      },
      {
        "lag": 5,
        "acf": -0.08561,
        "p_value": 0.3943,
        "critical_value": 0.197
      },
      {
        "lag": 6,
        "acf": 0.00142,
        "p_value": 0.9887,
        "critical_value": 0.197
      },
      {
        "lag": 7,
        "acf": 0.07288,
        "p_value": 0.4684,
        "critical_value": 0.197
      },
      {
        "lag": 8,
        "acf": 0.1069,
        "p_value": 0.2875,
        "critical_value": 0.197
      },
      {
        "lag": 9,
        "acf": 0.0913,
        "p_value": 0.3637,
        "critical_value": 0.197
      },
      {
        "lag": 10,
        "acf": 0.09913,
        "p_value": 0.324,
        "critical_value": 0.197
      },
      {
        "lag": 11,
        "acf": 0.09495,
        "p_value": 0.3448,
        "critical_value": 0.197
      },
      {
        "lag": 12,
        "acf": 0.09163,
        "p_value": 0.3619,
        "critical_value": 0.197
      },
      {
        "lag": 13,
        "acf": 0.04043,
        "p_value": 0.6875,
        "critical_value": 0.197
      },
      {
        "lag": 14,
        "acf": -0.04395,
        "p_value": 0.6619,
        "critical_value": 0.197
      },
      {
        "lag": 15,
        "acf": 0.02277,
        "p_value": 0.8208,
        "critical_value": 0.197
      },
      {
        "lag": 16,
        "acf": 0.04113,
        "p_value": 0.6823,
        "critical_value": 0.197
      },
      {
        "lag": 17,
        "acf": 0.005567,
        "p_value": 0.9558,
        "critical_value": 0.197
      },
      {
        "lag": 18,
        "acf": 0.04269,
        "p_value": 0.671,
        "critical_value": 0.197
      },
      {
        "lag": 19,
        "acf": 0.0949,
        "p_value": 0.345,
        "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

data
REQUIREDarraydatasets: 1min data points: 10max data points: 10000

The time series data. An object in data represents 1 distinct time series. Keys must be encoded according to the ISO8601 date and time format subset RFC 3339, section 5.6. The value of existing data points must be a number, the value of missing data points must be encoded as null.

imputation
optionalstringdefault: linear
valid values: linear, spline, stineman, mean, median, mode, locf, nocb, sma, lwma, ewma, kalman

Imputation of missing values. Argument ignored if no missing values exist.

transformation
optionalobject

Performs (automatic) transformations of the time series data prior to the main analysis to fulfill parametric model assumptions.

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.

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).

precision
optionalobject

Decimal point precision of the output data.

RETURNS

report.computation_time

The actual and billed computation time of the invocation in milliseconds.

result.arguments

The applied arguments.

In rare cases, the applied arguments can deviate from the arguments of the request. To make this fully transparent, the applied arguments are returned with each response.

For example, result.arguments.imputation is returned as null, if no missing values exist in the time series data of the request, to indicate that no imputation was applied.

For example, if a taper is selected that is incompatible with the method, it is replaced by a compatible taper.

result.imputation

The imputed missing values and the corresponding time indices.

result.transformation

The performed data transformations.

If a transformation was not applied, it is returned as null in result.transformation.

For example, if the arguments period and seasonal_differences of the request are both auto and are both returned as null in result.transformation, this implies that no dominant frequency has been found to determine the period and thus no seasonal differencing has been applied.

result.data

The output of the statistical computation.

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

If first_differences + seasonal_differences * period (in result.transformation) > 0, result.data starts with initial null values of the corresponding length.

{
  "data": [
    {
      "2020-01-01T00:00:00Z": 1.0137,
      "2020-01-01T00:00:01Z": 0.8591,
      "2020-01-01T00:00:02Z": 0.6281,
      "2020-01-01T00:00:03Z": 0.0703,
      "2020-01-01T00:00:04Z": -1.2546,
      "2020-01-01T00:00:05Z": 0.0635,
      "2020-01-01T00:00:06Z": 0.9731,
      "2020-01-01T00:00:07Z": 1.1618,
      "2020-01-01T00:00:08Z": 2.5978,
      "2020-01-01T00:00:09Z": 3.9978,
      "2020-01-01T00:00:10Z": 4.0237,
      "2020-01-01T00:00:11Z": 4.6535,
      "2020-01-01T00:00:12Z": 5.0346,
      "2020-01-01T00:00:13Z": 4.8492,
      "2020-01-01T00:00:14Z": 5.3419,
      "2020-01-01T00:00:15Z": 5.0351,
      "2020-01-01T00:00:16Z": 3.7687,
      "2020-01-01T00:00:17Z": 3.374,
      "2020-01-01T00:00:18Z": 1.1942,
      "2020-01-01T00:00:19Z": -1.0547,
      "2020-01-01T00:00:20Z": -3.3157,
      "2020-01-01T00:00:21Z": -5.057,
      "2020-01-01T00:00:22Z": -6.691,
      "2020-01-01T00:00:23Z": -7.6573,
      "2020-01-01T00:00:24Z": -7.6522,
      "2020-01-01T00:00:25Z": -7.2028,
      "2020-01-01T00:00:26Z": -5.7701,
      "2020-01-01T00:00:27Z": -4.5187,
      "2020-01-01T00:00:28Z": -3.7872,
      "2020-01-01T00:00:29Z": -4.2919,
      "2020-01-01T00:00:30Z": -3.8214,
      "2020-01-01T00:00:31Z": -4.195,
      "2020-01-01T00:00:32Z": -3.5719,
      "2020-01-01T00:00:33Z": -2.4975,
      "2020-01-01T00:00:34Z": -2.787,
      "2020-01-01T00:00:35Z": -3.6928,
      "2020-01-01T00:00:36Z": -3.2771,
      "2020-01-01T00:00:37Z": -3.8647,
      "2020-01-01T00:00:38Z": -2.9803,
      "2020-01-01T00:00:39Z": -3.6646,
      "2020-01-01T00:00:40Z": -2.829,
      "2020-01-01T00:00:41Z": -3.1812,
      "2020-01-01T00:00:42Z": -2.3828,
      "2020-01-01T00:00:43Z": -2.7223,
      "2020-01-01T00:00:44Z": -2.7717,
      "2020-01-01T00:00:45Z": -1.8045,
      "2020-01-01T00:00:46Z": -0.5042,
      "2020-01-01T00:00:47Z": 1.3069,
      "2020-01-01T00:00:48Z": 2.7687,
      "2020-01-01T00:00:49Z": 3.9865,
      "2020-01-01T00:00:50Z": 2.7695,
      "2020-01-01T00:00:51Z": 3.1204,
      "2020-01-01T00:00:52Z": 4.742,
      "2020-01-01T00:00:53Z": 7.6089,
      "2020-01-01T00:00:54Z": 9.054,
      "2020-01-01T00:00:55Z": 9.3756,
      "2020-01-01T00:00:56Z": 10.36,
      "2020-01-01T00:00:57Z": 11.1193,
      "2020-01-01T00:00:58Z": 11.5563,
      "2020-01-01T00:00:59Z": 13.6662,
      "2020-01-01T00:01:00Z": 15.6862,
      "2020-01-01T00:01:01Z": 18.0665,
      "2020-01-01T00:01:02Z": 19.3616,
      "2020-01-01T00:01:03Z": 19.8506,
      "2020-01-01T00:01:04Z": 20.7675,
      "2020-01-01T00:01:05Z": 20.6054,
      "2020-01-01T00:01:06Z": 19.2565,
      "2020-01-01T00:01:07Z": 18.536,
      "2020-01-01T00:01:08Z": 19.3415,
      "2020-01-01T00:01:09Z": 21.0423,
      "2020-01-01T00:01:10Z": 23.8812,
      "2020-01-01T00:01:11Z": 25.6965,
      "2020-01-01T00:01:12Z": 27.7823,
      "2020-01-01T00:01:13Z": 26.512,
      "2020-01-01T00:01:14Z": 26.2565,
      "2020-01-01T00:01:15Z": 26.0911,
      "2020-01-01T00:01:16Z": 25.4152,
      "2020-01-01T00:01:17Z": 24.8234,
      "2020-01-01T00:01:18Z": 23.2512,
      "2020-01-01T00:01:19Z": 24.0036,
      "2020-01-01T00:01:20Z": 24.9257,
      "2020-01-01T00:01:21Z": 25.5759,
      "2020-01-01T00:01:22Z": 27.1171,
      "2020-01-01T00:01:23Z": 28.4398,
      "2020-01-01T00:01:24Z": 28.5233,
      "2020-01-01T00:01:25Z": 26.8893,
      "2020-01-01T00:01:26Z": 25.8306,
      "2020-01-01T00:01:27Z": 25.2715,
      "2020-01-01T00:01:28Z": 24.0688,
      "2020-01-01T00:01:29Z": 24.6046,
      "2020-01-01T00:01:30Z": 24.6625,
      "2020-01-01T00:01:31Z": 24.1545,
      "2020-01-01T00:01:32Z": 23.4331,
      "2020-01-01T00:01:33Z": 22.8225,
      "2020-01-01T00:01:34Z": 20.5345,
      "2020-01-01T00:01:35Z": 21.5842,
      "2020-01-01T00:01:36Z": 22.3886,
      "2020-01-01T00:01:37Z": 23.4767,
      "2020-01-01T00:01:38Z": 22.5141,
      "2020-01-01T00:01:39Z": 23.3534
    }
  ],
  "imputation": "linear",
  "transformation": {
    "period": "auto",
    "box_cox_lambda": "auto",
    "seasonal_differences": "auto",
    "first_differences": "auto"
  },
  "method": "direct",
  "taper": "rectangle",
  "conversion": null,
  "precision": {
    "digits": 4,
    "method": "significant"
  }
}
{
  "report": {
    "computation_time": {
      "actual": 1104.61,
      "billed": 1200
    }
  },
  "result": {
    "arguments": {
      "imputation": null,
      "transformation": {
        "period": "auto",
        "box_cox_lambda": "auto",
        "seasonal_differences": "auto",
        "first_differences": "auto"
      },
      "method": "direct",
      "taper": "rectangle",
      "conversion": null,
      "precision": {
        "digits": 4,
        "method": "significant"
      }
    },
    "imputation": [],
    "transformation": {
      "period": null,
      "box_cox_lambda": 1.072,
      "seasonal_differences": null,
      "first_differences": 1
    },
    "data": [
      {
        "frequency": 0.005051,
        "spectral_density": 2.026
      },
      {
        "frequency": 0.0101,
        "spectral_density": 12.03
      },
      {
        "frequency": 0.01515,
        "spectral_density": 15.29
      },
      {
        "frequency": 0.0202,
        "spectral_density": 4.532
      },
      {
        "frequency": 0.02525,
        "spectral_density": 0.1604
      },
      {
        "frequency": 0.0303,
        "spectral_density": 1.537
      },
      {
        "frequency": 0.03535,
        "spectral_density": 0.9134
      },
      {
        "frequency": 0.0404,
        "spectral_density": 5.306
      },
      {
        "frequency": 0.04545,
        "spectral_density": 4.645
      },
      {
        "frequency": 0.05051,
        "spectral_density": 2.494
      },
      {
        "frequency": 0.05556,
        "spectral_density": 6.094
      },
      {
        "frequency": 0.06061,
        "spectral_density": 1.944
      },
      {
        "frequency": 0.06566,
        "spectral_density": 3.96
      },
      {
        "frequency": 0.07071,
        "spectral_density": 5.472
      },
      {
        "frequency": 0.07576,
        "spectral_density": 0.9924
      },
      {
        "frequency": 0.08081,
        "spectral_density": 2.963
      },
      {
        "frequency": 0.08586,
        "spectral_density": 5.195
      },
      {
        "frequency": 0.09091,
        "spectral_density": 5.994
      },
      {
        "frequency": 0.09596,
        "spectral_density": 4.691
      },
      {
        "frequency": 0.101,
        "spectral_density": 1.905
      },
      {
        "frequency": 0.1061,
        "spectral_density": 7.043
      },
      {
        "frequency": 0.1111,
        "spectral_density": 9.594
      },
      {
        "frequency": 0.1162,
        "spectral_density": 2.6
      },
      {
        "frequency": 0.1212,
        "spectral_density": 1.457
      },
      {
        "frequency": 0.1263,
        "spectral_density": 1.042
      },
      {
        "frequency": 0.1313,
        "spectral_density": 1.229
      },
      {
        "frequency": 0.1364,
        "spectral_density": 3.34
      },
      {
        "frequency": 0.1414,
        "spectral_density": 4.955
      },
      {
        "frequency": 0.1465,
        "spectral_density": 3.021
      },
      {
        "frequency": 0.1515,
        "spectral_density": 0.002885
      },
      {
        "frequency": 0.1566,
        "spectral_density": 2.189
      },
      {
        "frequency": 0.1616,
        "spectral_density": 2.238
      },
      {
        "frequency": 0.1667,
        "spectral_density": 1.305
      },
      {
        "frequency": 0.1717,
        "spectral_density": 0.9568
      },
      {
        "frequency": 0.1768,
        "spectral_density": 0.6499
      },
      {
        "frequency": 0.1818,
        "spectral_density": 1.392
      },
      {
        "frequency": 0.1869,
        "spectral_density": 2.471
      },
      {
        "frequency": 0.1919,
        "spectral_density": 1.179
      },
      {
        "frequency": 0.197,
        "spectral_density": 0.007676
      },
      {
        "frequency": 0.202,
        "spectral_density": 0.2946
      },
      {
        "frequency": 0.2071,
        "spectral_density": 0.4469
      },
      {
        "frequency": 0.2121,
        "spectral_density": 0.167
      },
      {
        "frequency": 0.2172,
        "spectral_density": 0.1747
      },
      {
        "frequency": 0.2222,
        "spectral_density": 0.2085
      },
      {
        "frequency": 0.2273,
        "spectral_density": 0.6255
      },
      {
        "frequency": 0.2323,
        "spectral_density": 1.033
      },
      {
        "frequency": 0.2374,
        "spectral_density": 0.1914
      },
      {
        "frequency": 0.2424,
        "spectral_density": 0.2707
      },
      {
        "frequency": 0.2475,
        "spectral_density": 0.2275
      },
      {
        "frequency": 0.2525,
        "spectral_density": 2.336
      },
      {
        "frequency": 0.2576,
        "spectral_density": 2.444
      },
      {
        "frequency": 0.2626,
        "spectral_density": 0.7067
      },
      {
        "frequency": 0.2677,
        "spectral_density": 0.5255
      },
      {
        "frequency": 0.2727,
        "spectral_density": 0.9868
      },
      {
        "frequency": 0.2778,
        "spectral_density": 0.4454
      },
      {
        "frequency": 0.2828,
        "spectral_density": 0.4075
      },
      {
        "frequency": 0.2879,
        "spectral_density": 0.5831
      },
      {
        "frequency": 0.2929,
        "spectral_density": 0.3748
      },
      {
        "frequency": 0.298,
        "spectral_density": 1.255
      },
      {
        "frequency": 0.303,
        "spectral_density": 0.3925
      },
      {
        "frequency": 0.3081,
        "spectral_density": 0.4154
      },
      {
        "frequency": 0.3131,
        "spectral_density": 0.08261
      },
      {
        "frequency": 0.3182,
        "spectral_density": 2.19
      },
      {
        "frequency": 0.3232,
        "spectral_density": 1.3
      },
      {
        "frequency": 0.3283,
        "spectral_density": 0.2591
      },
      {
        "frequency": 0.3333,
        "spectral_density": 1.573
      },
      {
        "frequency": 0.3384,
        "spectral_density": 0.2642
      },
      {
        "frequency": 0.3434,
        "spectral_density": 0.1474
      },
      {
        "frequency": 0.3485,
        "spectral_density": 0.09259
      },
      {
        "frequency": 0.3535,
        "spectral_density": 0.3539
      },
      {
        "frequency": 0.3586,
        "spectral_density": 0.4893
      },
      {
        "frequency": 0.3636,
        "spectral_density": 0.1363
      },
      {
        "frequency": 0.3687,
        "spectral_density": 0.1883
      },
      {
        "frequency": 0.3737,
        "spectral_density": 0.3974
      },
      {
        "frequency": 0.3788,
        "spectral_density": 0.7665
      },
      {
        "frequency": 0.3838,
        "spectral_density": 1.056
      },
      {
        "frequency": 0.3889,
        "spectral_density": 1.059
      },
      {
        "frequency": 0.3939,
        "spectral_density": 0.7648
      },
      {
        "frequency": 0.399,
        "spectral_density": 0.5565
      },
      {
        "frequency": 0.404,
        "spectral_density": 0.6852
      },
      {
        "frequency": 0.4091,
        "spectral_density": 0.2997
      },
      {
        "frequency": 0.4141,
        "spectral_density": 0.1506
      },
      {
        "frequency": 0.4192,
        "spectral_density": 0.04216
      },
      {
        "frequency": 0.4242,
        "spectral_density": 0.09078
      },
      {
        "frequency": 0.4293,
        "spectral_density": 0.9092
      },
      {
        "frequency": 0.4343,
        "spectral_density": 2.132
      },
      {
        "frequency": 0.4394,
        "spectral_density": 1.045
      },
      {
        "frequency": 0.4444,
        "spectral_density": 0.3081
      },
      {
        "frequency": 0.4495,
        "spectral_density": 0.1914
      },
      {
        "frequency": 0.4545,
        "spectral_density": 0.3538
      },
      {
        "frequency": 0.4596,
        "spectral_density": 0.396
      },
      {
        "frequency": 0.4646,
        "spectral_density": 0.05386
      },
      {
        "frequency": 0.4697,
        "spectral_density": 1.187
      },
      {
        "frequency": 0.4747,
        "spectral_density": 3.282
      },
      {
        "frequency": 0.4798,
        "spectral_density": 1.54
      },
      {
        "frequency": 0.4848,
        "spectral_density": 0.1088
      },
      {
        "frequency": 0.4899,
        "spectral_density": 1.348
      },
      {
        "frequency": 0.4949,
        "spectral_density": 0.5312
      },
      {
        "frequency": 0.5,
        "spectral_density": 0.1508
      }
    ]
  }
}
{
  "report": {
    "computation_time": {
      "actual": 1104.61,
      "billed": 1200
    }
  },
  "result": {
    "arguments": {
      "imputation": null,
      "transformation": {
        "period": "auto",
        "box_cox_lambda": "auto",
        "seasonal_differences": "auto",
        "first_differences": "auto"
      },
      "method": "direct",
      "taper": "rectangle",
      "conversion": null,
      "precision": {
        "digits": 4,
        "method": "significant"
      }
    },
    "imputation": [],
    "transformation": {
      "period": null,
      "box_cox_lambda": 1.072,
      "seasonal_differences": null,
      "first_differences": 1
    },
    "data": [
      {
        "frequency": 0.005051,
        "spectral_density": 2.026
      },
      {
        "frequency": 0.0101,
        "spectral_density": 12.03
      },
      {
        "frequency": 0.01515,
        "spectral_density": 15.29
      },
      {
        "frequency": 0.0202,
        "spectral_density": 4.532
      },
      {
        "frequency": 0.02525,
        "spectral_density": 0.1604
      },
      {
        "frequency": 0.0303,
        "spectral_density": 1.537
      },
      {
        "frequency": 0.03535,
        "spectral_density": 0.9134
      },
      {
        "frequency": 0.0404,
        "spectral_density": 5.306
      },
      {
        "frequency": 0.04545,
        "spectral_density": 4.645
      },
      {
        "frequency": 0.05051,
        "spectral_density": 2.494
      },
      {
        "frequency": 0.05556,
        "spectral_density": 6.094
      },
      {
        "frequency": 0.06061,
        "spectral_density": 1.944
      },
      {
        "frequency": 0.06566,
        "spectral_density": 3.96
      },
      {
        "frequency": 0.07071,
        "spectral_density": 5.472
      },
      {
        "frequency": 0.07576,
        "spectral_density": 0.9924
      },
      {
        "frequency": 0.08081,
        "spectral_density": 2.963
      },
      {
        "frequency": 0.08586,
        "spectral_density": 5.195
      },
      {
        "frequency": 0.09091,
        "spectral_density": 5.994
      },
      {
        "frequency": 0.09596,
        "spectral_density": 4.691
      },
      {
        "frequency": 0.101,
        "spectral_density": 1.905
      },
      {
        "frequency": 0.1061,
        "spectral_density": 7.043
      },
      {
        "frequency": 0.1111,
        "spectral_density": 9.594
      },
      {
        "frequency": 0.1162,
        "spectral_density": 2.6
      },
      {
        "frequency": 0.1212,
        "spectral_density": 1.457
      },
      {
        "frequency": 0.1263,
        "spectral_density": 1.042
      },
      {
        "frequency": 0.1313,
        "spectral_density": 1.229
      },
      {
        "frequency": 0.1364,
        "spectral_density": 3.34
      },
      {
        "frequency": 0.1414,
        "spectral_density": 4.955
      },
      {
        "frequency": 0.1465,
        "spectral_density": 3.021
      },
      {
        "frequency": 0.1515,
        "spectral_density": 0.002885
      },
      {
        "frequency": 0.1566,
        "spectral_density": 2.189
      },
      {
        "frequency": 0.1616,
        "spectral_density": 2.238
      },
      {
        "frequency": 0.1667,
        "spectral_density": 1.305
      },
      {
        "frequency": 0.1717,
        "spectral_density": 0.9568
      },
      {
        "frequency": 0.1768,
        "spectral_density": 0.6499
      },
      {
        "frequency": 0.1818,
        "spectral_density": 1.392
      },
      {
        "frequency": 0.1869,
        "spectral_density": 2.471
      },
      {
        "frequency": 0.1919,
        "spectral_density": 1.179
      },
      {
        "frequency": 0.197,
        "spectral_density": 0.007676
      },
      {
        "frequency": 0.202,
        "spectral_density": 0.2946
      },
      {
        "frequency": 0.2071,
        "spectral_density": 0.4469
      },
      {
        "frequency": 0.2121,
        "spectral_density": 0.167
      },
      {
        "frequency": 0.2172,
        "spectral_density": 0.1747
      },
      {
        "frequency": 0.2222,
        "spectral_density": 0.2085
      },
      {
        "frequency": 0.2273,
        "spectral_density": 0.6255
      },
      {
        "frequency": 0.2323,
        "spectral_density": 1.033
      },
      {
        "frequency": 0.2374,
        "spectral_density": 0.1914
      },
      {
        "frequency": 0.2424,
        "spectral_density": 0.2707
      },
      {
        "frequency": 0.2475,
        "spectral_density": 0.2275
      },
      {
        "frequency": 0.2525,
        "spectral_density": 2.336
      },
      {
        "frequency": 0.2576,
        "spectral_density": 2.444
      },
      {
        "frequency": 0.2626,
        "spectral_density": 0.7067
      },
      {
        "frequency": 0.2677,
        "spectral_density": 0.5255
      },
      {
        "frequency": 0.2727,
        "spectral_density": 0.9868
      },
      {
        "frequency": 0.2778,
        "spectral_density": 0.4454
      },
      {
        "frequency": 0.2828,
        "spectral_density": 0.4075
      },
      {
        "frequency": 0.2879,
        "spectral_density": 0.5831
      },
      {
        "frequency": 0.2929,
        "spectral_density": 0.3748
      },
      {
        "frequency": 0.298,
        "spectral_density": 1.255
      },
      {
        "frequency": 0.303,
        "spectral_density": 0.3925
      },
      {
        "frequency": 0.3081,
        "spectral_density": 0.4154
      },
      {
        "frequency": 0.3131,
        "spectral_density": 0.08261
      },
      {
        "frequency": 0.3182,
        "spectral_density": 2.19
      },
      {
        "frequency": 0.3232,
        "spectral_density": 1.3
      },
      {
        "frequency": 0.3283,
        "spectral_density": 0.2591
      },
      {
        "frequency": 0.3333,
        "spectral_density": 1.573
      },
      {
        "frequency": 0.3384,
        "spectral_density": 0.2642
      },
      {
        "frequency": 0.3434,
        "spectral_density": 0.1474
      },
      {
        "frequency": 0.3485,
        "spectral_density": 0.09259
      },
      {
        "frequency": 0.3535,
        "spectral_density": 0.3539
      },
      {
        "frequency": 0.3586,
        "spectral_density": 0.4893
      },
      {
        "frequency": 0.3636,
        "spectral_density": 0.1363
      },
      {
        "frequency": 0.3687,
        "spectral_density": 0.1883
      },
      {
        "frequency": 0.3737,
        "spectral_density": 0.3974
      },
      {
        "frequency": 0.3788,
        "spectral_density": 0.7665
      },
      {
        "frequency": 0.3838,
        "spectral_density": 1.056
      },
      {
        "frequency": 0.3889,
        "spectral_density": 1.059
      },
      {
        "frequency": 0.3939,
        "spectral_density": 0.7648
      },
      {
        "frequency": 0.399,
        "spectral_density": 0.5565
      },
      {
        "frequency": 0.404,
        "spectral_density": 0.6852
      },
      {
        "frequency": 0.4091,
        "spectral_density": 0.2997
      },
      {
        "frequency": 0.4141,
        "spectral_density": 0.1506
      },
      {
        "frequency": 0.4192,
        "spectral_density": 0.04216
      },
      {
        "frequency": 0.4242,
        "spectral_density": 0.09078
      },
      {
        "frequency": 0.4293,
        "spectral_density": 0.9092
      },
      {
        "frequency": 0.4343,
        "spectral_density": 2.132
      },
      {
        "frequency": 0.4394,
        "spectral_density": 1.045
      },
      {
        "frequency": 0.4444,
        "spectral_density": 0.3081
      },
      {
        "frequency": 0.4495,
        "spectral_density": 0.1914
      },
      {
        "frequency": 0.4545,
        "spectral_density": 0.3538
      },
      {
        "frequency": 0.4596,
        "spectral_density": 0.396
      },
      {
        "frequency": 0.4646,
        "spectral_density": 0.05386
      },
      {
        "frequency": 0.4697,
        "spectral_density": 1.187
      },
      {
        "frequency": 0.4747,
        "spectral_density": 3.282
      },
      {
        "frequency": 0.4798,
        "spectral_density": 1.54
      },
      {
        "frequency": 0.4848,
        "spectral_density": 0.1088
      },
      {
        "frequency": 0.4899,
        "spectral_density": 1.348
      },
      {
        "frequency": 0.4949,
        "spectral_density": 0.5312
      },
      {
        "frequency": 0.5,
        "spectral_density": 0.1508
      }
    ]
  }
}
        

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. Spectral entropy is the inverse of the Omega forecastability measure.

ARGUMENTS

data
REQUIREDarraydatasets: 1min data points: 10max data points: 10000

The time series data. An object in data represents 1 distinct time series. Keys must be encoded according to the ISO8601 date and time format subset RFC 3339, section 5.6. The value of existing data points must be a number, the value of missing data points must be encoded as null.

imputation
optionalstringdefault: linear
valid values: linear, spline, stineman, mean, median, mode, locf, nocb, sma, lwma, ewma, kalman

Imputation of missing values. Argument ignored if no missing values exist.

transformation
optionalobject

Performs (automatic) transformations of the time series data prior to the main analysis to fulfill parametric model assumptions.

For fast data, we recommend using the following arguments for maximum speed, consistent data transformations and error prevention (also see our tutorial on moving statistics for fast data streams ):

For (non-stationary) non-seasonal data:

{
  "period": null,
  "box_cox_lambda": null,
  "seasonal_differences": null,
  "first_differences": 1
}

For (non-stationary) seasonal data with a known period (for example 12):

{
  "period": 12,
  "box_cox_lambda": null,
  "seasonal_differences": 1,
  "first_differences": 1
}
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 floor(time series length / 2), if larger than time series length / 2.

precision
optionalobject

Decimal point precision of the output data.

RETURNS

report.computation_time

The actual and billed computation time of the invocation in milliseconds.

result.arguments

The applied arguments.

In rare cases, the applied arguments can deviate from the arguments of the request. To make this fully transparent, the applied arguments are returned with each response.

For example, result.arguments.imputation is returned as null, if no missing values exist in the time series data of the request, to indicate that no imputation was applied.

For example, the argument window_size is changed to floor(time series length / 2), if set to a value greater than time series length / 2.

For example, if a taper is selected that is incompatible with the method, it is replaced by a compatible taper.

result.imputation

The imputed missing values and the corresponding time indices.

result.transformation

The performed data transformations.

If a transformation was not applied, it is returned as null in result.transformation.

For example, if the arguments period and seasonal_differences of the request are both auto and are both returned as null in result.transformation, this implies that no dominant frequency has been found to determine the period and thus no seasonal differencing has been applied.

result.data

The output of the statistical computation.

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

If first_differences + seasonal_differences * period (in result.transformation) > 0, result.data starts with initial null values of the corresponding length.

The initial null values in result.data (following the ones corresponding to first_differences + seasonal_differences * period) correspond to the moving window. The length of this sequence is window_size (in result.arguments) - 1.

The total length of the initial null sequence is thus first_differences + seasonal_differences * period + window_size - 1.

{
  "data": [
    {
      "2020-01-01T00:00:00Z": 1.0137,
      "2020-01-01T00:00:01Z": 0.8591,
      "2020-01-01T00:00:02Z": 0.6281,
      "2020-01-01T00:00:03Z": 0.0703,
      "2020-01-01T00:00:04Z": -1.2546,
      "2020-01-01T00:00:05Z": 0.0635,
      "2020-01-01T00:00:06Z": 0.9731,
      "2020-01-01T00:00:07Z": 1.1618,
      "2020-01-01T00:00:08Z": 2.5978,
      "2020-01-01T00:00:09Z": 3.9978,
      "2020-01-01T00:00:10Z": 4.0237,
      "2020-01-01T00:00:11Z": 4.6535,
      "2020-01-01T00:00:12Z": 5.0346,
      "2020-01-01T00:00:13Z": 4.8492,
      "2020-01-01T00:00:14Z": 5.3419,
      "2020-01-01T00:00:15Z": 5.0351,
      "2020-01-01T00:00:16Z": 3.7687,
      "2020-01-01T00:00:17Z": 3.374,
      "2020-01-01T00:00:18Z": 1.1942,
      "2020-01-01T00:00:19Z": -1.0547,
      "2020-01-01T00:00:20Z": -3.3157,
      "2020-01-01T00:00:21Z": -5.057,
      "2020-01-01T00:00:22Z": -6.691,
      "2020-01-01T00:00:23Z": -7.6573,
      "2020-01-01T00:00:24Z": -7.6522,
      "2020-01-01T00:00:25Z": -7.2028,
      "2020-01-01T00:00:26Z": -5.7701,
      "2020-01-01T00:00:27Z": -4.5187,
      "2020-01-01T00:00:28Z": -3.7872,
      "2020-01-01T00:00:29Z": -4.2919,
      "2020-01-01T00:00:30Z": -3.8214,
      "2020-01-01T00:00:31Z": -4.195,
      "2020-01-01T00:00:32Z": -3.5719,
      "2020-01-01T00:00:33Z": -2.4975,
      "2020-01-01T00:00:34Z": -2.787,
      "2020-01-01T00:00:35Z": -3.6928,
      "2020-01-01T00:00:36Z": -3.2771,
      "2020-01-01T00:00:37Z": -3.8647,
      "2020-01-01T00:00:38Z": -2.9803,
      "2020-01-01T00:00:39Z": -3.6646,
      "2020-01-01T00:00:40Z": -2.829,
      "2020-01-01T00:00:41Z": -3.1812,
      "2020-01-01T00:00:42Z": -2.3828,
      "2020-01-01T00:00:43Z": -2.7223,
      "2020-01-01T00:00:44Z": -2.7717,
      "2020-01-01T00:00:45Z": -1.8045,
      "2020-01-01T00:00:46Z": -0.5042,
      "2020-01-01T00:00:47Z": 1.3069,
      "2020-01-01T00:00:48Z": 2.7687,
      "2020-01-01T00:00:49Z": 3.9865,
      "2020-01-01T00:00:50Z": 2.7695,
      "2020-01-01T00:00:51Z": 3.1204,
      "2020-01-01T00:00:52Z": 4.742,
      "2020-01-01T00:00:53Z": 7.6089,
      "2020-01-01T00:00:54Z": 9.054,
      "2020-01-01T00:00:55Z": 9.3756,
      "2020-01-01T00:00:56Z": 10.36,
      "2020-01-01T00:00:57Z": 11.1193,
      "2020-01-01T00:00:58Z": 11.5563,
      "2020-01-01T00:00:59Z": 13.6662,
      "2020-01-01T00:01:00Z": 15.6862,
      "2020-01-01T00:01:01Z": 18.0665,
      "2020-01-01T00:01:02Z": 19.3616,
      "2020-01-01T00:01:03Z": 19.8506,
      "2020-01-01T00:01:04Z": 20.7675,
      "2020-01-01T00:01:05Z": 20.6054,
      "2020-01-01T00:01:06Z": 19.2565,
      "2020-01-01T00:01:07Z": 18.536,
      "2020-01-01T00:01:08Z": 19.3415,
      "2020-01-01T00:01:09Z": 21.0423,
      "2020-01-01T00:01:10Z": 23.8812,
      "2020-01-01T00:01:11Z": 25.6965,
      "2020-01-01T00:01:12Z": 27.7823,
      "2020-01-01T00:01:13Z": 26.512,
      "2020-01-01T00:01:14Z": 26.2565,
      "2020-01-01T00:01:15Z": 26.0911,
      "2020-01-01T00:01:16Z": 25.4152,
      "2020-01-01T00:01:17Z": 24.8234,
      "2020-01-01T00:01:18Z": 23.2512,
      "2020-01-01T00:01:19Z": 24.0036,
      "2020-01-01T00:01:20Z": 24.9257,
      "2020-01-01T00:01:21Z": 25.5759,
      "2020-01-01T00:01:22Z": 27.1171,
      "2020-01-01T00:01:23Z": 28.4398,
      "2020-01-01T00:01:24Z": 28.5233,
      "2020-01-01T00:01:25Z": 26.8893,
      "2020-01-01T00:01:26Z": 25.8306,
      "2020-01-01T00:01:27Z": 25.2715,
      "2020-01-01T00:01:28Z": 24.0688,
      "2020-01-01T00:01:29Z": 24.6046,
      "2020-01-01T00:01:30Z": 24.6625,
      "2020-01-01T00:01:31Z": 24.1545,
      "2020-01-01T00:01:32Z": 23.4331,
      "2020-01-01T00:01:33Z": 22.8225,
      "2020-01-01T00:01:34Z": 20.5345,
      "2020-01-01T00:01:35Z": 21.5842,
      "2020-01-01T00:01:36Z": 22.3886,
      "2020-01-01T00:01:37Z": 23.4767,
      "2020-01-01T00:01:38Z": 22.5141,
      "2020-01-01T00:01:39Z": 23.3534
    }
  ],
  "imputation": "linear",
  "transformation": {
    "period": "auto",
    "box_cox_lambda": "auto",
    "seasonal_differences": "auto",
    "first_differences": "auto"
  },
  "method": "direct",
  "taper": "rectangle",
  "window_size": 10,
  "precision": {
    "digits": 4,
    "method": "significant"
  }
}
{
  "report": {
    "computation_time": {
      "actual": 1279.5,
      "billed": 1300
    }
  },
  "result": {
    "arguments": {
      "imputation": null,
      "transformation": {
        "period": "auto",
        "box_cox_lambda": "auto",
        "seasonal_differences": "auto",
        "first_differences": "auto"
      },
      "method": "direct",
      "taper": "rectangle",
      "window_size": 10,
      "precision": {
        "digits": 4,
        "method": "significant"
      }
    },
    "imputation": [],
    "transformation": {
      "period": null,
      "box_cox_lambda": 1.072,
      "seasonal_differences": null,
      "first_differences": 1
    },
    "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": 0.7676
      },
      {
        "t": "2020-01-01T00:00:11Z",
        "spectral_entropy": 0.864
      },
      {
        "t": "2020-01-01T00:00:12Z",
        "spectral_entropy": 0.7942
      },
      {
        "t": "2020-01-01T00:00:13Z",
        "spectral_entropy": 0.8238
      },
      {
        "t": "2020-01-01T00:00:14Z",
        "spectral_entropy": 0.7778
      },
      {
        "t": "2020-01-01T00:00:15Z",
        "spectral_entropy": 0.9112
      },
      {
        "t": "2020-01-01T00:00:16Z",
        "spectral_entropy": 0.863
      },
      {
        "t": "2020-01-01T00:00:17Z",
        "spectral_entropy": 0.8237
      },
      {
        "t": "2020-01-01T00:00:18Z",
        "spectral_entropy": 0.8868
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}
        

statistical moments

POST /invocation/statistical-moments

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 signal detection for critical transitions and are differently associated with the dynamical phenomena of rising memory, rising variability and flickering.

ARGUMENTS

data
REQUIREDarraydatasets: 1min data points: 10max data points: 10000

The time series data. An object in data represents 1 distinct time series. Keys must be encoded according to the ISO8601 date and time format subset RFC 3339, section 5.6. The value of existing data points must be a number, the value of missing data points must be encoded as null.

imputation
optionalstringdefault: linear
valid values: linear, spline, stineman, mean, median, mode, locf, nocb, sma, lwma, ewma, kalman

Imputation of missing values. Argument ignored if no missing values exist.

transformation
optionalobject

Performs (automatic) transformations of the time series data prior to the main analysis to fulfill parametric model assumptions.

For fast data, we recommend using the following arguments for maximum speed, consistent data transformations and error prevention (also see our tutorial on moving statistics for fast data streams ):

For (non-stationary) non-seasonal data:

{
  "period": null,
  "box_cox_lambda": null,
  "seasonal_differences": null,
  "first_differences": 1
}

For (non-stationary) seasonal data with a known period (for example 12):

{
  "period": 12,
  "box_cox_lambda": null,
  "seasonal_differences": 1,
  "first_differences": 1
}
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 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 floor(time series length / 2), if larger than time series length / 2.

precision
optionalobject

Decimal point precision of the output data.

RETURNS

report.computation_time

The actual and billed computation time of the invocation in milliseconds.

result.arguments

The applied arguments.

In rare cases, the applied arguments can deviate from the arguments of the request. To make this fully transparent, the applied arguments are returned with each response.

For example, result.arguments.imputation is returned as null, if no missing values exist in the time series data of the request, to indicate that no imputation was applied.

For example, the argument window_size is changed to floor(time series length / 2), if set to a value greater than time series length / 2.

result.imputation

The imputed missing values and the corresponding time indices.

result.transformation

The performed data transformations.

If a transformation was not applied, it is returned as null in result.transformation.

For example, if the arguments period and seasonal_differences of the request are both auto and are both returned as null in result.transformation, this implies that no dominant frequency has been found to determine the period and thus no seasonal differencing has been applied.

result.data

The output of the statistical computation.

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

If first_differences + seasonal_differences * period (in result.transformation) > 0, result.data starts with initial null values of the corresponding length.

The initial null values in result.data (following the ones corresponding to first_differences + seasonal_differences * period) correspond to the moving window. The length of this sequence is window_size (in result.arguments) - 1.

The total length of the initial null sequence is thus first_differences + seasonal_differences * period + window_size - 1.

{
  "data": [
    {
      "2020-01-01T00:00:00Z": 1.0137,
      "2020-01-01T00:00:01Z": 0.8591,
      "2020-01-01T00:00:02Z": 0.6281,
      "2020-01-01T00:00:03Z": 0.0703,
      "2020-01-01T00:00:04Z": -1.2546,
      "2020-01-01T00:00:05Z": 0.0635,
      "2020-01-01T00:00:06Z": 0.9731,
      "2020-01-01T00:00:07Z": 1.1618,
      "2020-01-01T00:00:08Z": 2.5978,
      "2020-01-01T00:00:09Z": 3.9978,
      "2020-01-01T00:00:10Z": 4.0237,
      "2020-01-01T00:00:11Z": 4.6535,
      "2020-01-01T00:00:12Z": 5.0346,
      "2020-01-01T00:00:13Z": 4.8492,
      "2020-01-01T00:00:14Z": 5.3419,
      "2020-01-01T00:00:15Z": 5.0351,
      "2020-01-01T00:00:16Z": 3.7687,
      "2020-01-01T00:00:17Z": 3.374,
      "2020-01-01T00:00:18Z": 1.1942,
      "2020-01-01T00:00:19Z": -1.0547,
      "2020-01-01T00:00:20Z": -3.3157,
      "2020-01-01T00:00:21Z": -5.057,
      "2020-01-01T00:00:22Z": -6.691,
      "2020-01-01T00:00:23Z": -7.6573,
      "2020-01-01T00:00:24Z": -7.6522,
      "2020-01-01T00:00:25Z": -7.2028,
      "2020-01-01T00:00:26Z": -5.7701,
      "2020-01-01T00:00:27Z": -4.5187,
      "2020-01-01T00:00:28Z": -3.7872,
      "2020-01-01T00:00:29Z": -4.2919,
      "2020-01-01T00:00:30Z": -3.8214,
      "2020-01-01T00:00:31Z": -4.195,
      "2020-01-01T00:00:32Z": -3.5719,
      "2020-01-01T00:00:33Z": -2.4975,
      "2020-01-01T00:00:34Z": -2.787,
      "2020-01-01T00:00:35Z": -3.6928,
      "2020-01-01T00:00:36Z": -3.2771,
      "2020-01-01T00:00:37Z": -3.8647,
      "2020-01-01T00:00:38Z": -2.9803,
      "2020-01-01T00:00:39Z": -3.6646,
      "2020-01-01T00:00:40Z": -2.829,
      "2020-01-01T00:00:41Z": -3.1812,
      "2020-01-01T00:00:42Z": -2.3828,
      "2020-01-01T00:00:43Z": -2.7223,
      "2020-01-01T00:00:44Z": -2.7717,
      "2020-01-01T00:00:45Z": -1.8045,
      "2020-01-01T00:00:46Z": -0.5042,
      "2020-01-01T00:00:47Z": 1.3069,
      "2020-01-01T00:00:48Z": 2.7687,
      "2020-01-01T00:00:49Z": 3.9865,
      "2020-01-01T00:00:50Z": 2.7695,
      "2020-01-01T00:00:51Z": 3.1204,
      "2020-01-01T00:00:52Z": 4.742,
      "2020-01-01T00:00:53Z": 7.6089,
      "2020-01-01T00:00:54Z": 9.054,
      "2020-01-01T00:00:55Z": 9.3756,
      "2020-01-01T00:00:56Z": 10.36,
      "2020-01-01T00:00:57Z": 11.1193,
      "2020-01-01T00:00:58Z": 11.5563,
      "2020-01-01T00:00:59Z": 13.6662,
      "2020-01-01T00:01:00Z": 15.6862,
      "2020-01-01T00:01:01Z": 18.0665,
      "2020-01-01T00:01:02Z": 19.3616,
      "2020-01-01T00:01:03Z": 19.8506,
      "2020-01-01T00:01:04Z": 20.7675,
      "2020-01-01T00:01:05Z": 20.6054,
      "2020-01-01T00:01:06Z": 19.2565,
      "2020-01-01T00:01:07Z": 18.536,
      "2020-01-01T00:01:08Z": 19.3415,
      "2020-01-01T00:01:09Z": 21.0423,
      "2020-01-01T00:01:10Z": 23.8812,
      "2020-01-01T00:01:11Z": 25.6965,
      "2020-01-01T00:01:12Z": 27.7823,
      "2020-01-01T00:01:13Z": 26.512,
      "2020-01-01T00:01:14Z": 26.2565,
      "2020-01-01T00:01:15Z": 26.0911,
      "2020-01-01T00:01:16Z": 25.4152,
      "2020-01-01T00:01:17Z": 24.8234,
      "2020-01-01T00:01:18Z": 23.2512,
      "2020-01-01T00:01:19Z": 24.0036,
      "2020-01-01T00:01:20Z": 24.9257,
      "2020-01-01T00:01:21Z": 25.5759,
      "2020-01-01T00:01:22Z": 27.1171,
      "2020-01-01T00:01:23Z": 28.4398,
      "2020-01-01T00:01:24Z": 28.5233,
      "2020-01-01T00:01:25Z": 26.8893,
      "2020-01-01T00:01:26Z": 25.8306,
      "2020-01-01T00:01:27Z": 25.2715,
      "2020-01-01T00:01:28Z": 24.0688,
      "2020-01-01T00:01:29Z": 24.6046,
      "2020-01-01T00:01:30Z": 24.6625,
      "2020-01-01T00:01:31Z": 24.1545,
      "2020-01-01T00:01:32Z": 23.4331,
      "2020-01-01T00:01:33Z": 22.8225,
      "2020-01-01T00:01:34Z": 20.5345,
      "2020-01-01T00:01:35Z": 21.5842,
      "2020-01-01T00:01:36Z": 22.3886,
      "2020-01-01T00:01:37Z": 23.4767,
      "2020-01-01T00:01:38Z": 22.5141,
      "2020-01-01T00:01:39Z": 23.3534
    }
  ],
  "imputation": "linear",
  "transformation": {
    "period": "auto",
    "box_cox_lambda": "auto",
    "seasonal_differences": "auto",
    "first_differences": "auto"
  },
  "method": "acf1",
  "window_size": 10,
  "precision": {
    "digits": 4,
    "method": "significant"
  }
}
{
  "report": {
    "computation_time": {
      "actual": 955.7,
      "billed": 1000
    }
  },
  "result": {
    "arguments": {
      "imputation": null,
      "transformation": {
        "period": "auto",
        "box_cox_lambda": "auto",
        "seasonal_differences": "auto",
        "first_differences": "auto"
      },
      "method": "acf1",
      "window_size": 10,
      "precision": {
        "digits": 4,
        "method": "significant"
      }
    },
    "imputation": [],
    "transformation": {
      "period": null,
      "box_cox_lambda": 1.072,
      "seasonal_differences": null,
      "first_differences": 1
    },
    "data": [
      {
        "t": "2020-01-01T00:00:00Z",
        "acf1": null
      },
      {
        "t": "2020-01-01T00:00:01Z",
        "acf1": null
      },
      {
        "t": "2020-01-01T00:00:02Z",
        "acf1": null
      },
      {
        "t": "2020-01-01T00:00:03Z",
        "acf1": null
      },
      {
        "t": "2020-01-01T00:00:04Z",
        "acf1": null
      },
      {
        "t": "2020-01-01T00:00:05Z",
        "acf1": null
      },
      {
        "t": "2020-01-01T00:00:06Z",
        "acf1": null
      },
      {
        "t": "2020-01-01T00:00:07Z",
        "acf1": null
      },
      {
        "t": "2020-01-01T00:00:08Z",
        "acf1": null
      },
      {
        "t": "2020-01-01T00:00:09Z",
        "acf1": null
      },
      {
        "t": "2020-01-01T00:00:10Z",
        "acf1": 0.2479
      },
      {
        "t": "2020-01-01T00:00:11Z",
        "acf1": 0.1918
      },
      {
        "t": "2020-01-01T00:00:12Z",
        "acf1": 0.1086
      },
      {
        "t": "2020-01-01T00:00:13Z",
        "acf1": -0.1455
      },
      {
        "t": "2020-01-01T00:00:14Z",
        "acf1": 0.02214
      },
      {
        "t": "2020-01-01T00:00:15Z",
        "acf1": -0.009837
      },
      {
        "t": "2020-01-01T00:00:16Z",
        "acf1": 0.2478
      },
      {
        "t": "2020-01-01T00:00:17Z",
        "acf1": 0.4084
      },
      {
        "t": "2020-01-01T00:00:18Z",
        "acf1": 0.1804
      },
      {
        "t": "2020-01-01T00:00:19Z",
        "acf1": 0.4851
      },
      {
        "t": "2020-01-01T00:00:20Z",
        "acf1": 0.5305
      },
      {
        "t": "2020-01-01T00:00:21Z",
        "acf1": 0.5474
      },
      {
        "t": "2020-01-01T00:00:22Z",
        "acf1": 0.5551
      },
      {
        "t": "2020-01-01T00:00:23Z",
        "acf1": 0.3742
      },
      {
        "t": "2020-01-01T00:00:24Z",
        "acf1": 0.2208
      },
      {
        "t": "2020-01-01T00:00:25Z",
        "acf1": 0.4571
      },
      {
        "t": "2020-01-01T00:00:26Z",
        "acf1": 0.5779
      },
      {
        "t": "2020-01-01T00:00:27Z",
        "acf1": 0.7556
      },
      {
        "t": "2020-01-01T00:00:28Z",
        "acf1": 0.8072
      },
      {
        "t": "2020-01-01T00:00:29Z",
        "acf1": 0.7336
      },
      {
        "t": "2020-01-01T00:00:30Z",
        "acf1": 0.6352
      },
      {
        "t": "2020-01-01T00:00:31Z",
        "acf1": 0.4648
      },
      {
        "t": "2020-01-01T00:00:32Z",
        "acf1": 0.2274
      },
      {
        "t": "2020-01-01T00:00:33Z",
        "acf1": 0.1778
      },
      {
        "t": "2020-01-01T00:00:34Z",
        "acf1": 0.0612
      },
      {
        "t": "2020-01-01T00:00:35Z",
        "acf1": 0.2004
      },
      {
        "t": "2020-01-01T00:00:36Z",
        "acf1": -0.02369
      },
      {
        "t": "2020-01-01T00:00:37Z",
        "acf1": -0.2635
      },
      {
        "t": "2020-01-01T00:00:38Z",
        "acf1": -0.2845
      },
      {
        "t": "2020-01-01T00:00:39Z",
        "acf1": -0.3532
      },
      {
        "t": "2020-01-01T00:00:40Z",
        "acf1": -0.4039
      },
      {
        "t": "2020-01-01T00:00:41Z",
        "acf1": -0.4215
      },
      {
        "t": "2020-01-01T00:00:42Z",
        "acf1": -0.5616
      },
      {
        "t": "2020-01-01T00:00:43Z",
        "acf1": -0.6844
      },
      {
        "t": "2020-01-01T00:00:44Z",
        "acf1": -0.7571
      },
      {
        "t": "2020-01-01T00:00:45Z",
        "acf1": -0.7585
      },
      {
        "t": "2020-01-01T00:00:46Z",
        "acf1": -0.4258
      },
      {
        "t": "2020-01-01T00:00:47Z",
        "acf1": -0.07532
      },
      {
        "t": "2020-01-01T00:00:48Z",
        "acf1": 0.1747
      },
      {
        "t": "2020-01-01T00:00:49Z",
        "acf1": 0.3944
      },
      {
        "t": "2020-01-01T00:00:50Z",
        "acf1": 0.1405
      },
      {
        "t": "2020-01-01T00:00:51Z",
        "acf1": 0.2233
      },
      {
        "t": "2020-01-01T00:00:52Z",
        "acf1": 0.1794
      },
      {
        "t": "2020-01-01T00:00:53Z",
        "acf1": 0.2019
      },
      {
        "t": "2020-01-01T00:00:54Z",
        "acf1": 0.3007
      },
      {
        "t": "2020-01-01T00:00:55Z",
        "acf1": 0.2576
      },
      {
        "t": "2020-01-01T00:00:56Z",
        "acf1": 0.2559
      },
      {
        "t": "2020-01-01T00:00:57Z",
        "acf1": 0.2417
      },
      {
        "t": "2020-01-01T00:00:58Z",
        "acf1": 0.2368
      },
      {
        "t": "2020-01-01T00:00:59Z",
        "acf1": 0.1871
      },
      {
        "t": "2020-01-01T00:01:00Z",
        "acf1": 0.1578
      },
      {
        "t": "2020-01-01T00:01:01Z",
        "acf1": 0.3052
      },
      {
        "t": "2020-01-01T00:01:02Z",
        "acf1": 0.2763
      },
      {
        "t": "2020-01-01T00:01:03Z",
        "acf1": 0.3123
      },
      {
        "t": "2020-01-01T00:01:04Z",
        "acf1": 0.3858
      },
      {
        "t": "2020-01-01T00:01:05Z",
        "acf1": 0.35
      },
      {
        "t": "2020-01-01T00:01:06Z",
        "acf1": 0.4552
      },
      {
        "t": "2020-01-01T00:01:07Z",
        "acf1": 0.6372
      },
      {
        "t": "2020-01-01T00:01:08Z",
        "acf1": 0.6664
      },
      {
        "t": "2020-01-01T00:01:09Z",
        "acf1": 0.581
      },
      {
        "t": "2020-01-01T00:01:10Z",
        "acf1": 0.4919
      },
      {
        "t": "2020-01-01T00:01:11Z",
        "acf1": 0.6259
      },
      {
        "t": "2020-01-01T00:01:12Z",
        "acf1": 0.6686
      },
      {
        "t": "2020-01-01T00:01:13Z",
        "acf1": 0.3944
      },
      {
        "t": "2020-01-01T00:01:14Z",
        "acf1": 0.483
      },
      {
        "t": "2020-01-01T00:01:15Z",
        "acf1": 0.4455
      },
      {
        "t": "2020-01-01T00:01:16Z",
        "acf1": 0.4029
      },
      {
        "t": "2020-01-01T00:01:17Z",
        "acf1": 0.5095
      },
      {
        "t": "2020-01-01T00:01:18Z",
        "acf1": 0.5092
      },
      {
        "t": "2020-01-01T00:01:19Z",
        "acf1": 0.3432
      },
      {
        "t": "2020-01-01T00:01:20Z",
        "acf1": 0.1872
      },
      {
        "t": "2020-01-01T00:01:21Z",
        "acf1": -0.07015
      },
      {
        "t": "2020-01-01T00:01:22Z",
        "acf1": 0.3123
      },
      {
        "t": "2020-01-01T00:01:23Z",
        "acf1": 0.4965
      },
      {
        "t": "2020-01-01T00:01:24Z",
        "acf1": 0.4719
      },
      {
        "t": "2020-01-01T00:01:25Z",
        "acf1": 0.3547
      },
      {
        "t": "2020-01-01T00:01:26Z",
        "acf1": 0.4546
      },
      {
        "t": "2020-01-01T00:01:27Z",
        "acf1": 0.4272
      },
      {
        "t": "2020-01-01T00:01:28Z",
        "acf1": 0.6273
      },
      {
        "t": "2020-01-01T00:01:29Z",
        "acf1": 0.5369
      },
      {
        "t": "2020-01-01T00:01:30Z",
        "acf1": 0.5174
      },
      {
        "t": "2020-01-01T00:01:31Z",
        "acf1": 0.3995
      },
      {
        "t": "2020-01-01T00:01:32Z",
        "acf1": 0.1402
      },
      {
        "t": "2020-01-01T00:01:33Z",
        "acf1": -0.03867
      },
      {
        "t": "2020-01-01T00:01:34Z",
        "acf1": 0.1164
      },
      {
        "t": "2020-01-01T00:01:35Z",
        "acf1": -0.3384
      },
      {
        "t": "2020-01-01T00:01:36Z",
        "acf1": -0.07813
      },
      {
        "t": "2020-01-01T00:01:37Z",
        "acf1": 0.05148
      },
      {
        "t": "2020-01-01T00:01:38Z",
        "acf1": 0.02819
      },
      {
        "t": "2020-01-01T00:01:39Z",
        "acf1": -0.05922
      }
    ]
  }
}
{
  "report": {
    "computation_time": {
      "actual": 955.7,
      "billed": 1000
    }
  },
  "result": {
    "arguments": {
      "imputation": null,
      "transformation": {
        "period": "auto",
        "box_cox_lambda": "auto",
        "seasonal_differences": "auto",
        "first_differences": "auto"
      },
      "method": "acf1",
      "window_size": 10,
      "precision": {
        "digits": 4,
        "method": "significant"
      }
    },
    "imputation": [],
    "transformation": {
      "period": null,
      "box_cox_lambda": 1.072,
      "seasonal_differences": null,
      "first_differences": 1
    },
    "data": [
      {
        "t": "2020-01-01T00:00:00Z",
        "acf1": null
      },
      {
        "t": "2020-01-01T00:00:01Z",
        "acf1": null
      },
      {
        "t": "2020-01-01T00:00:02Z",
        "acf1": null
      },
      {
        "t": "2020-01-01T00:00:03Z",
        "acf1": null
      },
      {
        "t": "2020-01-01T00:00:04Z",
        "acf1": null
      },
      {
        "t": "2020-01-01T00:00:05Z",
        "acf1": null
      },
      {
        "t": "2020-01-01T00:00:06Z",
        "acf1": null
      },
      {
        "t": "2020-01-01T00:00:07Z",
        "acf1": null
      },
      {
        "t": "2020-01-01T00:00:08Z",
        "acf1": null
      },
      {
        "t": "2020-01-01T00:00:09Z",
        "acf1": null
      },
      {
        "t": "2020-01-01T00:00:10Z",
        "acf1": 0.2479
      },
      {
        "t": "2020-01-01T00:00:11Z",
        "acf1": 0.1918
      },
      {
        "t": "2020-01-01T00:00:12Z",
        "acf1": 0.1086
      },
      {
        "t": "2020-01-01T00:00:13Z",
        "acf1": -0.1455
      },
      {
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