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

Class AutoCovariance

java.lang.Object

com.numericalmethod.suanshu.analysis.function.matrix.R2toMatrix

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

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

All Implemented Interfaces:

Function<Vector,Matrix>, RntoMatrix, java.io.Serializable

public class AutoCovariance
extends AutoCovarianceFunction

Compute the Auto-CoVariance Function (ACVF) for a vector AutoRegressive Moving Average (ARMA) model, assuming that EX_t = 0.

This implementation solves the Yule-Walker equation.

The R equivalent function are ARMAacf and TacvfAR in package FitAR.

See Also:

"P. J. Brockwell and R. A. Davis, "p. 420. Eq. 11.3.15. The Covariance Matrix Function of a Causal ARMA Process. Chapter 11.3. Multivariate Time Series," in Time Series: Theory and Methods, Springer, 2006.", Serialized Form

Nested Class Summary

Nested classes/interfaces inherited from interface com.numericalmethod.suanshu.analysis.function.Function

Function.EvaluationException

Field Summary

Fields

Modifier and Type	Field and Description
int	nLags the number of lags in the result

Constructor Summary

Constructors

Constructor and Description
AutoCovariance(ARIMAModel model, int nLags) Compute the auto-covariance function of a vector ARMA model.

Method Summary

Modifier and Type	Method and Description
Matrix	evaluate(double i) Get the i-th auto-covariance matrix.
Matrix	evaluate(double x1, double x2) Evaluate f(x1, x2) = A.

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

get

Methods inherited from class com.numericalmethod.suanshu.analysis.function.matrix.R2toMatrix

dimensionOfDomain, dimensionOfRange, evaluate

Methods inherited from class java.lang.Object

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

Field Detail

nLags

public final int nLags

the number of lags in the result

Constructor Detail

AutoCovariance

public AutoCovariance(ARIMAModel model,
                      int nLags)

Compute the auto-covariance function of a vector ARMA model.

To solve Eq. 11.3.15, we "expand" the (p+1) matrix equations into (p+1)*m*m linear equations. m is the dimension of Gamma (ACVF).

Parameters:

model - an ARIMA specification

nLags - the number of lags in the result

Method Detail

evaluate

public Matrix evaluate(double x1,
                       double x2)

Description copied from class: R2toMatrix

Evaluate f(x₁, x₂) = A.

Specified by:

evaluate in class R2toMatrix

Parameters:

x1 - x1

x2 - x2

Returns:

f(x1, x2)

evaluate

public Matrix evaluate(double i)

Get the i-th auto-covariance matrix.

Parameters:

i - the lag

Returns:

the i-th auto-covariance matrix