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

java.lang.Object
  com.numericalmethod.suanshu.stats.timeseries.linear.multivariate.arima.VARIMAXModel
      com.numericalmethod.suanshu.stats.timeseries.linear.multivariate.stationaryprocess.arma.VARMAXModel
          com.numericalmethod.suanshu.stats.timeseries.linear.multivariate.stationaryprocess.arma.VARXModel

public class VARXModel
extends VARMAXModel

A VARX (Vector AutoRegressive model with eXogeneous inputs) model, X_t, takes this form. \[ Y_t = \mu + \Sigma \phi_i * Y_{t-i} + \Psi * D_t + \epsilon_t \] where Y_t, μ and ε_t are n-dimensional vectors. The n-by-n matrices {φ_i} (i = 1, 2, ..., p) denote the AR coefficients. D_t is an m-by-1 vector which contains all exogenous variables at time t (excluding the intercept term), and its coefficients are represented by an n-by-m matrix ψ.

This implementation provides conversion methods between a VARX(p) model and a VECM(p) model (long-run or transitory).

See Also:

• "S. Johansen, "ch. 2-4, pp. 11-88," Likelihood-Based Inference in Cointegrated Vector Autoregressive Models, Oxford, Oxford University Press, 1995."
• "S. Johansen and K. Juselius, Maximum Likelihood Estimation and Inference on Cointegration - with Applications to the Demand for Money, Oxford Bull. of Econ. and Stat, vol. 52, 169-210, 1990."

Constructor Summary

VARXModel(Matrix[] phi, Matrix psi)
Construct a VARX model with unit variance and zero-mean.

VARXModel(Matrix[] phi, Matrix psi, Matrix sigma)
Construct a VARX model with zero-mean.

VARXModel(VARXModel that)
Copy constructor.

VARXModel(VECMLongrun vecm)
Construct a VARX(p) from a long-run VECM(p).

VARXModel(VECMTransitory vecm)
Construct a VARX(p) from a transitory VECM(p).

VARXModel(Vector mu, Matrix[] phi, Matrix psi)
Construct a VARX model with unit variance.

VARXModel(Vector mu, Matrix[] phi, Matrix psi, Matrix sigma)
Construct a VARX model.

Method Summary

Methods inherited from class com.numericalmethod.suanshu.stats.timeseries.linear.multivariate.stationaryprocess.arma.VARMAXModel

armaxMean

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

VARXModel

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

Construct a VARX model.

Parameters:

mu - the intercept (constant) vector

phi - the AR coefficients (excluding the initial 1)

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

sigma - the white noise covariance matrix

VARXModel

public VARXModel(Vector mu,
                 Matrix[] phi,
                 Matrix psi)

Construct a VARX model with unit variance.

Parameters:

mu - the intercept (constant) vector

phi - the AR coefficients (excluding the initial 1)

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

VARXModel

public VARXModel(Matrix[] phi,
                 Matrix psi,
                 Matrix sigma)

Construct a VARX model with zero-mean.

Parameters:

phi - the AR coefficients (excluding the initial 1)

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

sigma - the white noise covariance matrix

VARXModel

public VARXModel(Matrix[] phi,
                 Matrix psi)

Construct a VARX model with unit variance and zero-mean.

Parameters:

phi - the AR coefficients (excluding the initial 1)

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

VARXModel

public VARXModel(VECMTransitory vecm)

Construct a VARX(p) from a transitory VECM(p).

Parameters:

vecm - a transitory VECM(p)

VARXModel

public VARXModel(VECMLongrun vecm)

Construct a VARX(p) from a long-run VECM(p).

Parameters:

vecm - a long-run VECM(p)

VARXModel

public VARXModel(VARXModel that)

Copy constructor.

Parameters:

that - a VARX model