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

java.lang.Object
  com.numericalmethod.suanshu.stats.timeseries.linear.multivariate.stationaryprocess.InnovationAlgorithmImpl
      com.numericalmethod.suanshu.stats.timeseries.linear.multivariate.stationaryprocess.InnovationAlgorithm

public class InnovationAlgorithm
extends InnovationAlgorithmImpl

The innovation algorithm is an efficient way of obtaining a one step least square linear predictor for a linear time series {X_t} with known covariance structure.

This implementation works for multivariate time series with known auto-covariance structure and these properties (not limited to ARMA processes):

• {X_t} can be non-stationary.
• E{X_t} = 0 for all t.

See Also:

• "P. J. Brockwell and R. A. Davis, "Proposition. 5.2.2. Chapter 5. Multivariate Time Series," 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."

Field Summary

Fields inherited from class com.numericalmethod.suanshu.stats.timeseries.linear.multivariate.stationaryprocess.InnovationAlgorithmImpl

XtHat

Constructor Summary

InnovationAlgorithm(MultiVariateTimeSeries Xt, AutoCovarianceFunction K)
Construct an instance of InnovationAlgorithm for a multivariate time series with known auto-covariance structure.

Method Summary

Methods inherited from class com.numericalmethod.suanshu.stats.timeseries.linear.multivariate.stationaryprocess.InnovationAlgorithmImpl

covariance, getTheta, run, XtHat, XtHat

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

InnovationAlgorithm

public InnovationAlgorithm(MultiVariateTimeSeries Xt,
                           AutoCovarianceFunction 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