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

Class ARMAXModel

java.lang.Object

com.numericalmethod.suanshu.stats.timeseries.linear.multivariate.arima.ARIMAXModel

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

All Implemented Interfaces:

java.io.Serializable

Direct Known Subclasses:

VARXModel

public class ARMAXModel
extends ARIMAXModel

This class represents a multivariate ARMAX (ARMA model with eXogenous inputs) model.

The multivariate ARMAX model incorporates exogenous variables and it can be considered as a generalization of the multivariate ARMA model. Let Y_t be a multivariate ARMAX process, then

Y_t = μ + Σ φ_i * Y_{t-i} + Σ θ_j * ε_{t-j} + ψ * D_t + ε_t.

In the equation above, Y_s, μ and ε_s are n-dimensional vectors; (n * n) matrices {φ_i} and {θ_j} are the AR and MA coefficients, respectively; D_t is an (m * 1) vector which contains all exogenous variables at time t (excl. the intercept term), and its coefficients are represented by a (n * m) matrix ψ.

See Also:

Wikipedia: Autoregressive moving average model - Generalizations, Serialized Form

Field Summary

Fields inherited from class com.numericalmethod.suanshu.stats.timeseries.linear.multivariate.arima.ARIMAXModel

mu, phi, psi, sigma, theta

Constructor Summary

Constructors

Constructor and Description
ARMAXModel(ARMAXModel that) Copy constructor.
ARMAXModel(ARMAXModel model) Cast a univariate ARMAX model to a multivariate model.
ARMAXModel(Matrix[] phi, Matrix[] theta, Matrix psi) Construct a zero-intercept (mu) multivariate ARMAX model with unit variance.
ARMAXModel(Matrix[] phi, Matrix[] theta, Matrix psi, Matrix sigma) Construct a zero-intercept (mu) multivariate ARMAX model.
ARMAXModel(Vector mu, Matrix[] phi, Matrix[] theta, Matrix psi) Construct a multivariate ARMAX model with unit variance.
ARMAXModel(Vector mu, Matrix[] phi, Matrix[] theta, Matrix psi, Matrix sigma) Construct a multivariate ARMAX (ARMA model with eXogenous inputs) model.

Method Summary

Modifier and Type	Method and Description
Matrix	armaxMean(Matrix arLags, Matrix maLags, Vector exVar) Compute the multivariate ARMAX conditional mean.
Matrix	armaxMeanNoIntercept(Matrix arLags, Matrix maLags, Vector exVar) Compute the zero-intercept (mu) multivariate ARMAX conditional mean.

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

AR, AR, d, dimension, getArmax, MA, MA, maxPQ, mu, p, psi, q, sigma

Methods inherited from class java.lang.Object

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

Constructor Detail

ARMAXModel

public ARMAXModel(Vector mu,
                  Matrix[] phi,
                  Matrix[] theta,
                  Matrix psi,
                  Matrix sigma)

Construct a multivariate ARMAX (ARMA model with eXogenous inputs) model.

Parameters:

mu - the intercept (constant) vector

phi - the AR coefficients (excluding the initial 1); null if no AR coefficient

theta - the MA coefficients (excluding the initial 1); null if no MA coefficient

psi - the coefficients of the deterministic terms (excluding the intercept term)

sigma - the covariance matrix of white noise

ARMAXModel

public ARMAXModel(Vector mu,
                  Matrix[] phi,
                  Matrix[] theta,
                  Matrix psi)

Construct a multivariate ARMAX model with unit variance.

Parameters:

mu - the intercept (constant) vector

phi - the AR coefficients (excluding the initial 1); null if no AR coefficient

theta - the MA coefficients (excluding the initial 1); null if no MA coefficient

psi - the coefficients of the deterministic terms (excluding the intercept term)

ARMAXModel

public ARMAXModel(Matrix[] phi,
                  Matrix[] theta,
                  Matrix psi,
                  Matrix sigma)

Construct a zero-intercept (mu) multivariate ARMAX model.

Parameters:

phi - the AR coefficients (excluding the initial 1); null if no AR coefficient

theta - the MA coefficients (excluding the initial 1); null if no MA coefficient

psi - the coefficients of the deterministic terms (excluding the intercept term)

sigma - the covariance matrix of white noise

ARMAXModel

public ARMAXModel(Matrix[] phi,
                  Matrix[] theta,
                  Matrix psi)

Construct a zero-intercept (mu) multivariate ARMAX model with unit variance.

Parameters:

phi - the AR coefficients (excluding the initial 1); null if no AR coefficient

theta - the MA coefficients (excluding the initial 1); null if no MA coefficient

psi - the coefficients of the deterministic terms (excluding the intercept term)

ARMAXModel

public ARMAXModel(ARMAXModel that)

Copy constructor.

Parameters:

that - a multivariate ARMAX model

ARMAXModel

public ARMAXModel(ARMAXModel model)

Cast a univariate ARMAX model to a multivariate model.

Parameters:

model - a univariate ARIMA model

Method Detail

armaxMeanNoIntercept

public Matrix armaxMeanNoIntercept(Matrix arLags,
                                   Matrix maLags,
                                   Vector exVar)

Compute the zero-intercept (mu) multivariate ARMAX conditional mean.

Parameters:

arLags - the AR lags

maLags - the MA lags

exVar - the exogenous variables

Returns:

the conditional mean

armaxMean

public Matrix armaxMean(Matrix arLags,
                        Matrix maLags,
                        Vector exVar)

Compute the multivariate ARMAX conditional mean.

Parameters:

arLags - the AR lags

maLags - the MA lags

exVar - the exogenous variables

Returns:

the conditional mean