# SuanShu, a Java numerical and statistical library

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

## Class ARMAXModel

• public class ARMAXModel
extends ARIMAXModel
The ARMAX model (ARIMA model with eXogenous inputs) is a generalization of the ARMA model by incorporating exogenous variables. Xt is an ARMAX(p, q) process, for which $X_t = \mu + \sum_{i=1}^p \phi_i X_{t-i} + \sum_{i=1}^q \theta_j \epsilon_{t-j} + \psi' D_t + \epsilon_t,$ where 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 m-dimensional vector ψ.
Wikipedia: Autoregressive moving average model with exogenous inputs model (ARMAX model)
• ### Constructor Summary

Constructors
Constructor and Description
ARMAXModel(ARMAXModel that)
Copy constructor.
ARMAXModel(double[] AR, double[] MA, double[] psi)
Construct a univariate ARMAX model with unit variance and zero-intercept (mu).
ARMAXModel(double[] AR, double[] MA, double[] psi, double sigma)
Construct a univariate ARMAX model with zero-intercept (mu).
ARMAXModel(double mu, double[] AR, double[] MA, double[] psi)
Construct a univariate ARMAX model with unit variance.
ARMAXModel(double mu, double[] AR, double[] MA, double[] psi, double sigma)
Construct a univariate ARMAX model.
• ### Constructor Detail

• #### ARMAXModel

public ARMAXModel(double mu,
double[] AR,
double[] MA,
double[] psi,
double sigma)
Construct a univariate ARMAX model.
Parameters:
mu - the intercept (constant) term
AR - the AR coefficients (excluding the initial 1); null if no AR coefficients
MA - the MA coefficients (excluding the initial 1); null if no MA coefficients
psi - the coefficients of the deterministic terms (excluding the intercept term)
sigma - the white noise variance
• #### ARMAXModel

public ARMAXModel(double mu,
double[] AR,
double[] MA,
double[] psi)
Construct a univariate ARMAX model with unit variance.
Parameters:
mu - the intercept (constant) term
AR - the AR coefficients (excluding the initial 1); null if no AR coefficients
MA - the MA coefficients (excluding the initial 1); null if no MA coefficients
psi - the coefficients of the deterministic terms (excluding the intercept term)
• #### ARMAXModel

public ARMAXModel(double[] AR,
double[] MA,
double[] psi,
double sigma)
Construct a univariate ARMAX model with zero-intercept (mu).
Parameters:
AR - the AR coefficients (excluding the initial 1); null if no AR coefficients
MA - the MA coefficients (excluding the initial 1); null if no MA coefficients
psi - the coefficients of the deterministic terms (excluding the intercept term)
sigma - the white noise variance
• #### ARMAXModel

public ARMAXModel(double[] AR,
double[] MA,
double[] psi)
Construct a univariate ARMAX model with unit variance and zero-intercept (mu).
Parameters:
AR - the AR coefficients (excluding the initial 1); null if no AR coefficients
MA - the MA coefficients (excluding the initial 1); null if no MA coefficients
psi - the coefficients of the deterministic terms (excluding the intercept term)
• #### ARMAXModel

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

• #### armaxMean

public double armaxMean(double[] arLags,
double[] maLags,
double[] exVar)
Compute the univariate ARMAX conditional mean.
Parameters:
arLags - the AR lags
maLags - the MA lags
exVar - the exogenous variables
Returns:
the conditional mean