# SuanShu, a Java numerical and statistical library

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

## Class MultivariateForecastOneStep

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

• public class MultivariateForecastOneStep
extends Object
The innovation algorithm is an efficient way to obtain a one step least square linear predictor for a multivariate linear time series with known auto-covariance and these properties (not limited to ARMA processes):
• {xt} can be non-stationary.
• E(xt) = 0 for all t.
• "P. J. Brockwell and R. A. Davis, "Proposition. 5.2.2. Chapter 5. Prediction of Stationary Processes," in Time Series: Theory and Methods, Springer, 2006."
• "P. J. Brockwell and R. A. Davis, "Proposition. 11.4.2. Chapter 11.4 Best Linear Predictors of Second Order Random Vectors," in Time Series: Theory and Methods, Springer, 2006."
• ### Constructor Summary

Constructors
Constructor and Description
MultivariateForecastOneStep(MultivariateIntTimeTimeSeries Xt, MultivariateAutoCovarianceFunction K)
Construct an instance of InnovationAlgorithm for a multivariate time series with known auto-covariance structure.
• ### 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

• #### MultivariateForecastOneStep

public MultivariateForecastOneStep(MultivariateIntTimeTimeSeries Xt,
MultivariateAutoCovarianceFunction K)
Construct an instance of InnovationAlgorithm for a multivariate time series with known auto-covariance structure.
Parameters:
Xt - an m-dimensional time series, length t
K - auto-covariance function K(i, j) = E(Xi * Xj'), a m x m matrix
• ### 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