BUILT-IN MATHEMATICA SYMBOL

# TimeSeriesForecast

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]s[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:
• TimeSeriesForecast supports a Method option with the following settings:
•  Automatic automatically 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.

## ExamplesExamplesopen allclose all

### Basic Examples (3)Basic Examples (3)

Forecast the next step ahead with an ARProcess:

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Forecast 4 steps ahead with a MAProcess:

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Predict the seventh value for an ARMAProcess:

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Mean squared error of the forecast:

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