# SuanShu, a Java numerical and statistical library

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

## Class VARMAXModel

• Direct Known Subclasses:
VARXModel

public class VARMAXModel
extends VARIMAXModel
The VARMAX model (ARMA model with eXogenous inputs) is a generalization of the ARMA model by incorporating exogenous variables. Xt is an ARMAX(p, q) process, for which $X_t = \mu + \sum \phi_i X_{t-i} + \sum \theta_j \epsilon_{t-j} + \psi' D_t + \epsilon_t,$ Xt, μ and εt are n-dimensional vectors. The (n * n) matrices $${\phi_i}$$ and $${\theta_j}$$ are the AR and MA coefficients respectively. Dt is an (m * 1) vector which contains all exogenous variables at time t (excluding the intercept term), and its coefficients are represented by an (n * m) matrix ψ.
See Also:
Wikipedia: Autoregressive moving average model - Generalizations
• ### Constructor Summary

Constructors
Constructor and Description
VARMAXModel(ARMAXModel model)
Construct a multivariate model from a univariate ARMAX model.
VARMAXModel(Matrix[] phi, Matrix[] theta, Matrix psi)
Construct a multivariate ARMAX model with unit variance and zero-intercept (mu).
VARMAXModel(Matrix[] phi, Matrix[] theta, Matrix psi, Matrix sigma)
Construct a multivariate ARMAX model with zero-intercept (mu).
VARMAXModel(VARMAXModel that)
Copy constructor.
VARMAXModel(Vector mu, Matrix[] phi, Matrix[] theta, Matrix psi)
Construct a multivariate ARMAX model with unit variance.
VARMAXModel(Vector mu, Matrix[] phi, Matrix[] theta, Matrix psi, Matrix sigma)
Construct a multivariate ARMAX model.
• ### Method Summary

All Methods
Modifier and Type Method and Description
Matrix armaxMean(Matrix arLags, Matrix maLags, Vector exVar)
Compute the multivariate ARMAX conditional mean.
• ### Methods inherited from class com.numericalmethod.suanshu.stats.timeseries.linear.multivariate.arima.VARIMAXModel

AR, d, dimension, getVARMAX, MA, maxPQ, mu, p, phi, psi, q, sigma, theta
• ### Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
• ### Constructor Detail

• #### VARMAXModel

public VARMAXModel(Vector mu,
Matrix[] phi,
Matrix[] theta,
Matrix psi,
Matrix sigma)
Construct a multivariate ARMAX 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 white noise covariance matrix
• #### VARMAXModel

public VARMAXModel(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)
• #### VARMAXModel

public VARMAXModel(Matrix[] phi,
Matrix[] theta,
Matrix psi,
Matrix sigma)
Construct a multivariate ARMAX model with zero-intercept (mu).
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 white noise covariance matrix
• #### VARMAXModel

public VARMAXModel(Matrix[] phi,
Matrix[] theta,
Matrix psi)
Construct a multivariate ARMAX model with unit variance and zero-intercept (mu).
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)
• #### VARMAXModel

public VARMAXModel(ARMAXModel model)
Construct a multivariate model from a univariate ARMAX model.
Parameters:
model - a univariate ARIMA model
• #### VARMAXModel

public VARMAXModel(VARMAXModel that)
Copy constructor.
Parameters:
that - a multivariate ARMAX model
• ### Method Detail

• #### 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

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