com.numericalmethod.suanshu.stats.timeseries.linear.univariate.stationaryprocess.arima
Class ArimaSim

java.lang.Object
  com.numericalmethod.suanshu.stats.timeseries.univariate.realtime.SimpleTimeSeries
      com.numericalmethod.suanshu.stats.timeseries.linear.univariate.stationaryprocess.arima.ArimaSim

All Implemented Interfaces:

TimeSeries<java.lang.Integer,java.lang.Double>

public class ArimaSim
extends SimpleTimeSeries

This class simulates the ARIMA models.

An AutoRegressive Integrated Moving Average (ARIMA) model is a generalization of an AutoRegressive Moving Average (ARMA) model. They are applied in some cases where data show evidence of non-stationarity, where an initial differencing step (corresponding to the "integrated" part of the model) can be applied to remove the non-stationarity.

Given a time series of data Xt, the ARMA model is a tool for understanding and, perhaps, predicting future values in this series. The model consists of two parts, an autoregressive (AR) part and a moving average (MA) part. The model is usually then referred to as the ARMA(p,q) model where p is the order of the autoregressive part and q is the order of the moving average part.

The notation AR(p) refers to the autoregressive model of order p. The AR(p) model is defined as the weighted sum of the lagged values, a constant, and a white noise.

The notation MA(q) refers to the autoregressive model of order q. The MA(q) model is defined as the weighted sum of the lagged white noises and a drift. That is, a moving average model is conceptually a linear regression of the current value of the series against previous (unobserved) white noise error terms or random shocks. The random shocks are suppose to propagate to future values of the time series.

See Also:

• Wikipedia: Autoregressive integrated moving average
• Wikipedia: Autoregressive moving average model
• Wikipedia: Autoregressive model
• Wikipedia: Moving average model
• "P. J. Brockwell and R. A. Davis, "Chapter 9. Model Building and Forecasting with ARIMA Processes," in Time Series: Theory and Methods, Springer, 2006."

Nested Class Summary

Nested classes/interfaces inherited from class com.numericalmethod.suanshu.stats.timeseries.univariate.realtime.SimpleTimeSeries

SimpleTimeSeries.Iterator

Nested classes/interfaces inherited from interface com.numericalmethod.suanshu.stats.timeseries.univariate.realtime.TimeSeries

TimeSeries.Entry

Constructor Summary

ArimaSim(int n, ArimaModel arima)
Simulate an ARIMA model.

ArimaSim(int n, ArimaModel arima, Innovations innovations)
Simulate an ARIMA model.

Method Summary

Methods inherited from class com.numericalmethod.suanshu.stats.timeseries.univariate.realtime.SimpleTimeSeries

diff, drop, equals, get, hashCode, iterator, lag, lag, size, toArray, toString

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Constructor Detail

ArimaSim

public ArimaSim(int n,
                ArimaModel arima,
                Innovations innovations)

Simulate an ARIMA model.

The innovation length is at least

n + max(AR.length, MA.length) + d

Parameters:

n - the length of the time series to generate

arima - an ARIMA model

innovations - the innovations

ArimaSim

public ArimaSim(int n,
                ArimaModel arima)

Simulate an ARIMA model. The random error terms are from the standard Normal distribution.

Parameters:

n - the length of the time series to generate

arima - an ARIMA model