TimeSeriesForecast

TimeSeriesForecast[tproc,data,k]
gives the k-step-ahead forecast beyond data according to the time series process tproc.

TimeSeriesForecast[tsmod,k]
gives the k-step-ahead forecast for TimeSeriesModel tsmod.

Details and OptionsDetails and Options

  • TimeSeriesForecast[tproc,{x0,,xm},k] will give Expectation[x[m+k]x[0]x0x[m]xm], where xtproc, the expected value of the process given data.
  • TimeSeriesForecast allows tproc to be a time series process such as ARProcess, ARMAProcess, SARIMAProcess, etc.
  • The data can be a list of numeric values {x1,x2,}, a list of time-value pairs {{t1,x1},{t2,x2},}, or TemporalData.
  • The following forecast specifications can be given:
  • kat the k^(th) step ahead
    {kmax}at 1, , kmax steps ahead
    {kmin,kmax}at kmin, , kmax steps ahead
    {{k1,k2,}}use explicit {k1,k2,} steps ahead
  • TimeSeriesForecast returns the forecasted value if k is an integer and TemporalData otherwise.
  • The default for k is 1.
  • TimeSeriesForecast supports a Method option with the following settings:
  • Automaticautomatically determine the method
    "AR"approximate with a large-order AR process
    "Covariance"exact covariance function-based
    "Kalman"use Kalman filter
  • The mean squared errors of the prediction are the compounded noise errors and are given as MetaInformation in the TemporalData output. For forecast=TimeSeriesForecast[tproc,data,k], the mean squared errors can be accessed by forecast["MeanSquaredErrors"].

ExamplesExamplesopen allclose all

Basic Examples  (3)Basic Examples  (3)

Forecast three steps ahead for an ARProcess:

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An ARMAProcess:

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Predict the seventh value from TimeSeriesModel:

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Mean squared error of the forecast:

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Forecast a vector-valued time series process:

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Find the forecast for the next 10 steps:

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Plot the data and the forecast for each component:

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Introduced in 2012
(9.0)
| Updated in 2014
(10.0)
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