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

Class InnovationAlgorithmImpl

java.lang.Object

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

All Implemented Interfaces:

java.io.Serializable

Direct Known Subclasses:

InnovationAlgorithm, InnovationAlgorithm

public abstract class InnovationAlgorithmImpl
extends java.lang.Object
implements java.io.Serializable

This class implements the part of the innovation algorithm that computes the prediction coefficients, V and Θ. Subclasses implement the actual prediction algorithms for XtHat.

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."

, Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
protected MultiVariateTimeSeries	XtHat the one-step ahead predictors, {X^t+1}

Constructor Summary

Constructors

Modifier	Constructor and Description
protected	InnovationAlgorithmImpl()

Method Summary

Modifier and Type	Method and Description
ImmutableMatrix	covariance(int t) Get the covariance matrix for prediction errors at time t for X^t+1.
protected void	run(int t, AutoCovarianceFunction K) Run the Innovation Algorithm to compute the prediction parameters.
ImmutableMatrix	theta(int i, int j) Get the coefficients of the linear predictor.
MultiVariateTimeSeries	XtHat() Get all the one-step predictions X^t+1, t ∈ [0, t]
ImmutableVector	XtHat(int t) Get the one-step prediction X^t+1.

Methods inherited from class java.lang.Object

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

Field Detail

XtHat

protected MultiVariateTimeSeries XtHat

the one-step ahead predictors, {X^_t+1}

Constructor Detail

InnovationAlgorithmImpl

protected InnovationAlgorithmImpl()

Method Detail

run

protected void run(int t,
                   AutoCovarianceFunction K)

Run the Innovation Algorithm to compute the prediction parameters. This computes the prediction parameters, V and Θ.

Parameters:

t - time series length

K - the covariance structure of the time series

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 t)

Get the covariance matrix for prediction errors at time t for X^_t+1.

Parameters:

t - time, ranging from 0 to t

Returns:

the covariance matrix for prediction errors at time t

XtHat

public ImmutableVector XtHat(int t)

Get the one-step prediction X^_t+1.

Parameters:

t - time, ranging from 0 to t

Returns:

the one-step prediction X^_t+1

XtHat

public MultiVariateTimeSeries XtHat()

Get all the one-step predictions X^_t+1, t ∈ [0, t]

Returns:

all the one-step predictions