dev.nm.stat.timeseries.linear.univariate.stationaryprocess.arma

Class ARMAForecastOneStep

java.lang.Object

dev.nm.stat.timeseries.linear.univariate.stationaryprocess.arma.ARMAForecastOneStep

public class ARMAForecastOneStep
extends Object

Computes the one-step ahead prediction of a causal ARMA model, by the innovative algorithm.

See Also:

"P. J. Brockwell and R. A. Davis, "Section 5.3, Chapter 5, Recursive Prediction of an ARMA(p, q) Process," Time Series: Theory and Methods, Springer, 2006."

Constructor Summary

Constructors

Constructor and Description
ARMAForecastOneStep(double[] xt, ARMAModel arma) Makes the one-step ahead prediction for an ARMA model.
ARMAForecastOneStep(IntTimeTimeSeries xt, ARMAModel arma) Makes the one-step ahead prediction for an ARMA model.
ARMAForecastOneStep(IntTimeTimeSeries xt, ARMAModel arma, InnovationsAlgorithm inn) Makes the one-step ahead prediction for an ARMA model.

Method Summary

Modifier and Type	Method and Description
static AutoCovarianceFunction	K(ARMAModel arma)
double	var() Gets the mean squared error of the one-step ahead prediction.
double	var(int n) Gets the mean squared error of the prediction at time n for \(\hat{x}_{n+1}\), i.e., \(E(x_{n+1} - \hat{x}_{n+1})^2\).
double	xHat() Gets the one-step ahead prediction of the time series.
double	xHat(int n) Gets the one-step ahead prediction \(\hat{x}_{n+1}\).

Methods inherited from class java.lang.Object

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

Constructor Detail

ARMAForecastOneStep

public ARMAForecastOneStep(IntTimeTimeSeries xt,
                           ARMAModel arma,
                           InnovationsAlgorithm inn)

Makes the one-step ahead prediction for an ARMA model.

Parameters:

xt - the observations

arma - the ARMA model

inn - the innovation algorithm to use

ARMAForecastOneStep

public ARMAForecastOneStep(IntTimeTimeSeries xt,
                           ARMAModel arma)

Makes the one-step ahead prediction for an ARMA model.

Parameters:

xt - the observations

arma - the ARMA model

ARMAForecastOneStep

public ARMAForecastOneStep(double[] xt,
                           ARMAModel arma)

Makes the one-step ahead prediction for an ARMA model.

Parameters:

xt - the observations

arma - the ARMA model

Method Detail

K

public static AutoCovarianceFunction K(ARMAModel arma)

xHat

public double xHat(int n)

Gets the one-step ahead prediction \(\hat{x}_{n+1}\).

Parameters:

n - time, ranging from 0 to T, the end of observation time

Returns:

the one-step prediction \(\hat{x}_{n+1}\)

See Also:

"eq. 5.3.9"

var

public double var(int n)

Gets the mean squared error of the prediction at time n for \(\hat{x}_{n+1}\), i.e., \(E(x_{n+1} - \hat{x}_{n+1})^2\).

Parameters:

n - time, ranging from 0 to T, the end of observation time

Returns:

the mean squared error (variance)

xHat

public double xHat()

Gets the one-step ahead prediction of the time series.

Returns:

the one-step ahead prediction

var

public double var()

Gets the mean squared error of the one-step ahead prediction.

Returns:

the mean squared error (variance)