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

Class ARMAForecast

java.lang.Object

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

public class ARMAForecast
extends Object

Forecasts an ARMA time series using the innovative algorithm.

Forecast lifecycle

1. Put equally spaced observations in chronological order in an IntTimeTimeSeries; the first observation has time index one.
2. Supply an ARMAModel, or use the order-based constructor to fit an ARMA(p,q) model with CSS. That constructor does not select p or q.
3. Request a positive horizon with next(int). The returned Java list uses zero-based indices; the first forecast time is sample size plus one.

This is a stateful horizon iterator over a fixed observation history. Calling next(2) and then next() returns horizons one and two, then horizon three. It does not assimilate either actual observations or the previous prediction as a newly observed value. For a rolling forecast, construct a new forecaster with the newly extended history; do not mutate the old history while its forecaster is in use. Use independent instances for independent streams.

Check forecast values for finiteness. This example uses unit innovation variance; see the scaling note on ARMAForecastMultiStep before interpreting error variances for a non-unit model.

A supplied AR(1) model

With coefficient one half and zero intercept, each additional point forecast halves the last known value. These are conditional forecasts for a fixed model, not a fitted trading strategy.

 import dev.nm.stat.timeseries.datastructure.univariate.realtime.inttime.SimpleTimeSeries;
 import dev.nm.stat.timeseries.linear.univariate.stationaryprocess.arma.ARMAModel;
 import dev.nm.stat.timeseries.linear.univariate.stationaryprocess.arma.ARMAForecast;
 import dev.nm.stat.timeseries.linear.univariate.arima.ARIMAForecast.Forecast;
 import java.util.List;
 ARMAModel model = new ARMAModel(new double[]{0.5}, null);
 ARMAForecast forecast = new ARMAForecast(new SimpleTimeSeries(new double[]{1, 2, 3, 4}), model);
 List<Forecast> firstTwo = forecast.next(2);
 assert firstTwo.size() == 2;
 assert firstTwo.get(0).time() == 5;
 assert Math.abs(firstTwo.get(0).xHat() - 2) < 1e-10;
 assert Math.abs(firstTwo.get(1).xHat() - 1) < 1e-10;
 Forecast third = forecast.next();
 assert third.time() == 7;
 assert Math.abs(third.xHat() - 0.5) < 1e-10;
 assert Math.abs(firstTwo.get(0).var() - 1) < 1e-10;
 

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
ARMAForecast(IntTimeTimeSeries xt, ARMAModel arma) Constructs a forecaster for a time series assuming ARMA model.
ARMAForecast(IntTimeTimeSeries xt, int p, int q) Constructs a forecaster for a time series assuming ARMA model.

Method Summary

Modifier and Type	Method and Description
ARIMAForecast.Forecast	next() Gets the next forecast.
List<ARIMAForecast.Forecast>	next(int nSteps) Gets the next n-step forecasts.

Methods inherited from class java.lang.Object

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

Constructor Detail

ARMAForecast

public ARMAForecast(IntTimeTimeSeries xt,
                    ARMAModel arma)

Constructs a forecaster for a time series assuming ARMA model.

Parameters:

xt - a time series

arma - the ARMA specification

ARMAForecast

public ARMAForecast(IntTimeTimeSeries xt,
                    int p,
                    int q)

Constructs a forecaster for a time series assuming ARMA model.

Parameters:

xt - a time series

p - the number of AR terms

q - the number of MA terms

Method Detail

next

public ARIMAForecast.Forecast next()

Gets the next forecast.

Returns:

the next forecast

next

public List<ARIMAForecast.Forecast> next(int nSteps)

Gets the next n-step forecasts.

Parameters:

nSteps - the number of steps to forecast

Returns:

all the n-step forecasts