TimeSeriesForecast[tproc, data]
gives the one step ahead forecast for the time series tproc given data.

TimeSeriesForecast[tproc, data, kspec]
gives a forecast for the steps ahead specified by kspec.

Details and OptionsDetails and Options

  • TimeSeriesForecast[tproc, {s0, ..., sm}, k] will give Expectation[s[m+k]Conditioneds[0]=s0...s[m]=sm], where , the expected value of the process given the historical outcomes.
  • In TimeSeriesForecast[data], data can be given in the following forms:
  • {s0,...}a path with state at time i
    {{t0,s0},...}a path with state at time
    TemporalData[...]one or several paths
  • The times and states must belong to the time and state domain of the process tproc.
  • TimeSeriesForecast[tproc, data] returns the value of the one step ahead forecast.
  • TimeSeriesForecast[tproc, data, kspec] returns the forecast specified by kspec as TemporalData.
  • The following specifications can be given for kspec:
  • kat the k^(th) step ahead
    {kmax}at steps ahead
    {kmin,kmax}at steps ahead
    {{k1,k2,...}}use explicit steps ahead
  • 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 , the mean squared errors can be accessed by forecast.
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