# SuanShu, a Java numerical and statistical library

com.numericalmethod.suanshu.stats.timeseries.linear.multivariate.stationaryprocess.arma

## Class VARMAForecastOneStep

• java.lang.Object
• com.numericalmethod.suanshu.stats.timeseries.linear.multivariate.stationaryprocess.arma.VARMAForecastOneStep

• public class VARMAForecastOneStep
extends Object
This is an implementation, adapted for an ARMA process, of the innovation algorithm, which is an efficient way of obtaining a one step least square linear predictor.
• "P. J. Brockwell and R. A. Davis, "Chapter 5.3, Recursive Prediction of an ARMA(p,q) Process," Time Series: Theory and Methods, Springer, 2006."
• "P. J. Brockwell and R. A. Davis, "Eqs. 11.4.26, 11.4.27, 11.4.28, Chapter 11.4, Recursive Prediction of an ARMA(p,q) Process, Best Linear Predictors of Second Order Random Vectors," Time Series: Theory and Methods, Springer, 2006."
• ### Constructor Summary

Constructors
Constructor and Description
VARMAForecastOneStep(MultivariateIntTimeTimeSeries Xt, VARMAModel model)
Construct an instance of InnovationAlgorithm for a multivariate ARMA time series.
• ### Method Summary

All Methods
Modifier and Type Method and Description
ImmutableMatrix covariance(int n)
Get the covariance matrix for prediction errors for $$\hat{x}_{n+1}$$, made at time n.
ImmutableMatrix theta(int i, int j)
Get the coefficients of the linear predictor.
ImmutableVector xHat(int n)
Get the one-step prediction $$\hat{X}_{n+1} = P_{\mathfrak{S_n}}X_{n+1}$$, made at time n.
• ### Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
• ### Constructor Detail

• #### VARMAForecastOneStep

public VARMAForecastOneStep(MultivariateIntTimeTimeSeries Xt,
VARMAModel model)
Construct an instance of InnovationAlgorithm for a multivariate ARMA time series.
Parameters:
Xt - an m-dimensional time series
model - the ARMA model
• ### Method Detail

• #### xHat

public ImmutableVector xHat(int n)
Get the one-step prediction $$\hat{X}_{n+1} = P_{\mathfrak{S_n}}X_{n+1}$$, made at time n.
Parameters:
n - time, ranging from 0 to T, the end of observation time
Returns:
the one-step prediction $$\hat{X}_{n+1}$$
• #### theta

public ImmutableMatrix theta(int i,
int j)
Get the coefficients of the linear predictor.
Parameters:
i - i, ranging from 1 to t
j - j, ranging from 1 to t
Returns:
Θ[i][j]
• #### covariance

public ImmutableMatrix covariance(int n)
Get the covariance matrix for prediction errors for $$\hat{x}_{n+1}$$, made at time n.
Parameters:
n - time, ranging from 0 to T, the end of observation time
Returns:
the covariance matrix for prediction errors at time n