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

Class ARMAForecastMultiStep

java.lang.Object

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

public class ARMAForecastMultiStep
extends Object

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

Point forecasts and uncertainty

allForecasts() is indexed from one through the requested horizon, using NMDEV vector indices. Its first entry predicts sample size plus one. The forecast-error calculations are not a substitute for out-of-sample residual checks or an interval-calibration procedure.

Current scaling limitation: this implementation obtains a unit-variance demeaned model and divides innovation variances by the square of arma.sigma(). Since that model argument is documented as variance, do not assume var() or allMSEs() is in the original squared-data units for an arbitrary non-unit innovation variance. The runnable guide uses unit variance; point predictions and error scaling must be assessed separately.

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
ARMAForecastMultiStep(double[] xt, ARMAModel arma, int h) Makes the h-step ahead prediction for an ARMA model.
ARMAForecastMultiStep(IntTimeTimeSeries xt, ARMAModel arma) Makes the one-step ahead prediction for an ARMA model.
ARMAForecastMultiStep(IntTimeTimeSeries xt, ARMAModel arma, int h) Makes the h-step ahead prediction for an ARMA model.
ARMAForecastMultiStep(IntTimeTimeSeries xt, ARMAModel arma, int h, InnovationsAlgorithm inn) Makes the h-step ahead prediction for an ARMA model.
ARMAForecastMultiStep(IntTimeTimeSeries xt, ARMAModel arma, int h, InnovationsAlgorithm inn, ARMAForecastOneStep forecast1) Makes the h-step ahead prediction for an ARMA model.

Method Summary

Modifier and Type	Method and Description
Vector	allForecasts() Gets all the predictions of the next h steps in one vector.
Vector	allMSEs() Gets all the mean squared errors (MSE) of the h-step ahead predictions.
ARMAForecastOneStep	getARMAForecastOneStep() Gets the auxiliary ARMA one-step ahead forecaster.
InnovationsAlgorithm	getStandardError() Gets the the auxiliary coefficients, Θ and V, in using the innovative algorithm.
double	var() Gets the mean squared error of the h-step ahead prediction.
double	xHat() Gets the h-step ahead prediction of the time series.

Methods inherited from class java.lang.Object

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

Constructor Detail

ARMAForecastMultiStep

public ARMAForecastMultiStep(IntTimeTimeSeries xt,
                             ARMAModel arma,
                             int h,
                             InnovationsAlgorithm inn,
                             ARMAForecastOneStep forecast1)

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

Parameters:

xt - the observations

arma - the ARMA model

h - a time step

inn - the innovation algorithm to use

forecast1 - the auxiliary one-step ahead forecast of xt using arma

ARMAForecastMultiStep

public ARMAForecastMultiStep(IntTimeTimeSeries xt,
                             ARMAModel arma,
                             int h,
                             InnovationsAlgorithm inn)

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

Parameters:

xt - the observations

arma - the ARMA model

h - a time step

inn - the innovations

ARMAForecastMultiStep

public ARMAForecastMultiStep(IntTimeTimeSeries xt,
                             ARMAModel arma,
                             int h)

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

Parameters:

xt - the observations

arma - the ARMA model

h - a time step

ARMAForecastMultiStep

public ARMAForecastMultiStep(double[] xt,
                             ARMAModel arma,
                             int h)

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

Parameters:

xt - the observations

arma - the ARMA model

h - a time step

ARMAForecastMultiStep

public ARMAForecastMultiStep(IntTimeTimeSeries xt,
                             ARMAModel arma)

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

Parameters:

xt - the observations

arma - the ARMA model

Method Detail

xHat

public double xHat()

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

Returns:

the h-step ahead prediction

allForecasts

public Vector allForecasts()

Gets all the predictions of the next h steps in one vector.

Returns:

all the predictions of the next h steps

var

public double var()

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

Returns:

the mean squared error (variance)

allMSEs

public Vector allMSEs()

Gets all the mean squared errors (MSE) of the h-step ahead predictions.

Returns:

the mean squared errors (variance) of all h steps

getStandardError

public InnovationsAlgorithm getStandardError()

Gets the the auxiliary coefficients, Θ and V, in using the innovative algorithm.

Returns:

the the auxiliary coefficients, Θ and V, in using the innovative algorithm

getARMAForecastOneStep

public ARMAForecastOneStep getARMAForecastOneStep()

Gets the auxiliary ARMA one-step ahead forecaster.

Returns:

the auxiliary ARMA one-step ahead forecaster