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

java.lang.Object
  com.numericalmethod.suanshu.stats.timeseries.linear.multivariate.stationaryprocess.arima.arma.Vecm
      com.numericalmethod.suanshu.stats.timeseries.linear.multivariate.stationaryprocess.arima.arma.VecmLongrun

public class VecmLongrun
extends Vecm

This class represents a long-run Vector Error Correction Model (VECM).

A long-run vector error correction model (VECM(p)) has the following specification:

ΔY_t = μ + Π * Y_{t-p} + Σ[Γ_i * ΔY_{t-i}] + ψ * D_t + ε_t, (i = 1, 2, ..., p-1),

where Y_s, μ and ε_s are n-dimensional vectors; the impact matrix Π and the coefficients {Γ_i} of the lagged time series are (n * n) matrices; 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 a conversion method between a long-run VECM(p) and a VARX(p) model.

See Also:

• Wikipedia: Error correction model
• Wikipedia: Johansen test - The longrun VECM
• S. Johansen, “Likelihood-Based Inference in Cointegrated Vector Autoregressive Models,” Oxford, Oxford University Press, 1995, ch. 3-6, pp. 34-103.
• 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.

Constructor Summary

VecmLongrun(Matrix pi, Matrix[] gamma, Matrix psi, Matrix sigma)
Construct a zero-intercept (mu) long-run VECM(p) model.

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

VecmLongrun(VecmLongrun that)
Copy constructor.

VecmLongrun(Vector mu, Matrix pi, Matrix[] gamma, Matrix psi, Matrix sigma)
Construct a long-run VECM(p) model.

Method Summary

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

dimension, 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

VecmLongrun

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

Construct a long-run VECM(p) model.

Parameters:

mu - the intercept (constant) vector

pi - the impact matrix

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

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

sigma - the covariance matrix of white noise

VecmLongrun

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

Construct a zero-intercept (mu) long-run VECM(p) model.

Parameters:

pi - the impact matrix

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

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

sigma - the covariance matrix of white noise

VecmLongrun

public VecmLongrun(VarxModel varx)

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

Parameters:

varx - a VARX model

VecmLongrun

public VecmLongrun(VecmLongrun that)

Copy constructor.

Parameters:

that - a long-run VECM model