# 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 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:
•  k at the k 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:
•  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 forecast=TimeSeriesForecast[tproc,data,k], the mean squared errors can be accessed by forecast["MeanSquaredErrors"].

# Examples

open allclose all

## Basic Examples(3)

Forecast three steps ahead for an ARProcess:

 In[1]:=
 In[2]:=
 Out[2]=

An ARMAProcess:

 In[3]:=
 Out[3]=

Predict the seventh value from TimeSeriesModel:

 In[1]:=
 In[2]:=
 Out[2]=

Mean squared error of the forecast:

 In[3]:=
 Out[3]=

Forecast a vector-valued time series process:

 In[1]:=

Find the forecast for the next 10 steps:

 In[2]:=
 Out[2]=

Plot the data and the forecast for each component:

 In[3]:=
 Out[3]=