Package dev.nm.stat.timeseries.linear.multivariate.stationaryprocess.arma

Class VECMTransitory

java.lang.Object

dev.nm.stat.timeseries.linear.multivariate.stationaryprocess.arma.VECM

dev.nm.stat.timeseries.linear.multivariate.stationaryprocess.arma.VECMTransitory

public class VECMTransitory
extends VECM

A transitory Vector Error Correction Model (VECM(p)) takes this form. \[ \Delta Y_t = \mu + \Pi Y_{t-1} + \Sigma \left ( \Gamma_i Y_{t-1} \right ) + \Psi D_t + \epsilon_t, i = 1, 2, ..., p-1 \] Y_t, μ and ε_t are n-dimensional vectors. The impact matrix Π and the coefficients {Γ_i} of the lagged time series are n-by-n matrices; 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 a n-by-m matrix ψ.

This implementation provides a conversion method between a transitory VECM(p) and a VARX(p) model.

See Also:

• S. Johansen, "ch. 3-6, pp. 34-103," Likelihood-Based Inference in Cointegrated Vector Autoregressive Models, Oxford, Oxford University Press, 1995.
• S. Johansen, "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, vol. 59, 1551-1580, 1991.
• A. Banerjee et al., Cointegration, Error Correction, and the Econometric Analysis of Non-Stationary Data, Oxford, Oxford University Press, 1993.
• Wikipedia: Error correction model
• Wikipedia: Johansen test

Constructor Summary

Constructors

Constructor	Description
VECMTransitory(Matrix pi, Matrix[] gamma, Matrix psi, Matrix sigma)	Construct a transitory VECM(p) model with zero-intercept (mu).
VECMTransitory(Vector mu, Matrix pi, Matrix[] gamma, Matrix psi, Matrix sigma)	Construct a transitory VECM(p) model.
VECMTransitory(VARXModel varx)	Construct a transitory VECM(p) from a VARX(p).
VECMTransitory(VECMTransitory that)	Copy constructor.

Method Summary

Methods inherited from class dev.nm.stat.timeseries.linear.multivariate.stationaryprocess.arma.VECM

dimension, gamma, gamma, mu, p, pi, psi, sigma

Methods inherited from class java.lang.Object

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

Constructor Detail

VECMTransitory

public VECMTransitory(Vector mu,
                      Matrix pi,
                      Matrix[] gamma,
                      Matrix psi,
                      Matrix sigma)

Construct a transitory VECM(p) model.

Parameters:

mu - the intercept (constant) vector

pi - the impact matrix

gamma - the AR coefficients of the lagged differences; null if p = 1

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

sigma - the white noise covariance matrix

VECMTransitory

public VECMTransitory(Matrix pi,
                      Matrix[] gamma,
                      Matrix psi,
                      Matrix sigma)

Construct a transitory VECM(p) model with zero-intercept (mu).

Parameters:

pi - the impact matrix

gamma - the AR coefficients of the lagged differences; null if p = 1

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

sigma - the white noise covariance matrix

VECMTransitory

public VECMTransitory(VARXModel varx)

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

Parameters:

varx - a VARX model

VECMTransitory

public VECMTransitory(VECMTransitory that)

Copy constructor.

Parameters:

that - a transitory VECM model