com.numericalmethod.suanshu.stats.timeseries.linear.multivariate.stationaryprocess.arima.arma
Class VarxModel

java.lang.Object
  com.numericalmethod.suanshu.stats.timeseries.linear.multivariate.stationaryprocess.arima.ArimaxModel
      com.numericalmethod.suanshu.stats.timeseries.linear.multivariate.stationaryprocess.arima.arma.ArmaxModel
          com.numericalmethod.suanshu.stats.timeseries.linear.multivariate.stationaryprocess.arima.arma.VarxModel

public class VarxModel
extends ArmaxModel

This class represents a VARX (VAR model with eXogenous inputs) model.

The VARX (Vector AutoRegressive model with eXogeneous inputs) process Y_t has the following specification:

Y_t = μ + Σ φ_i * Y_{t-i} + ψ * D_t + ε_t,

where Y_s, μ and ε_s are n-dimensional vectors; (n * n) matrices {φ_i} (i = 1, 2, ..., p) denote the AR coefficients; 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.

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

See Also:

• S. Johansen, “Likelihood-Based Inference in Cointegrated Vector Autoregressive Models,” Oxford, Oxford University Press, 1995, ch. 2-4, pp. 11-88.
• 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.

Field Summary

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

mu, phi, psi, sigma, theta

Constructor Summary

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

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

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.arima.arma.ArmaxModel

armaxMean, armaxMeanNoIntercept

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

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 term)

sigma - the covariance matrix of white noise

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 term)

VarxModel

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

Construct a zero-mean VARX model.

Parameters:

phi - the AR coefficients (excluding the initial 1)

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

sigma - the covariance matrix of white noise

VarxModel

public VarxModel(Matrix[] phi,
                 Matrix psi)

Construct a zero-mean VARX model with unit variance.

Parameters:

phi - the AR coefficients (excluding the initial 1)

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

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