# SuanShu, a Java numerical and statistical library

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

## Class MultivariateInnovationAlgorithm

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

• public class MultivariateInnovationAlgorithm
extends Object
This class implements the part of the innovation algorithm that computes the prediction error covariances, V and prediction coefficients Θ. The coefficients depend only on the auto-covariance function and time horizon, not on any particular time series data.
• "P. J. Brockwell and R. A. Davis, "Proposition 5.2.2, Chapter 5, Multivariate Time Series," 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," Time Series: Theory and Methods, Springer, 2006."
• ### Constructor Summary

Constructors
Constructor and Description
MultivariateInnovationAlgorithm(int T, MultivariateAutoCovarianceFunction K)
Run the Innovation Algorithm to compute the prediction parameters, V and Θ.
• ### Method Summary

All Methods
Modifier and Type Method and Description
ImmutableMatrix covariance(int n)
Get the covariance matrix for prediction errors at time t for x^t+1.
ImmutableMatrix theta(int i, int j)
Get the coefficients of the linear predictor.
• ### Methods inherited from class java.lang.Object

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

• #### MultivariateInnovationAlgorithm

public MultivariateInnovationAlgorithm(int T,
MultivariateAutoCovarianceFunction K)
Run the Innovation Algorithm to compute the prediction parameters, V and Θ.
Parameters:
T - time series length
K - the covariance structure of the time series
• ### Method Detail

• #### theta

public ImmutableMatrix theta(int i,
int j)
Get the coefficients of the linear predictor.
Parameters:
i - i, ranging from 0 to T
j - j, ranging from 0 to T
Returns:
Θ[i][j]; Θ[?][0] = 1
• #### covariance

public ImmutableMatrix covariance(int n)
Get the covariance matrix for prediction errors at time t for x^t+1.
Parameters:
n - time, ranging from 0 to t, the end of observation time
Returns:
the covariance matrix for prediction errors at time n