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

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

public class VecmTransitory
extends Vecm

This class represents a transitory Vector Error Correction Model (VECM).

A transitory vector error correction model (VECM(p)) has the following specification:

ΔY_t = μ + Π * Y_{t-1} + 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 transitory VECM(p) and a VARX(p) model.

See Also:

• Wikipedia: Error correction model
• Wikipedia: Johansen test - The transitory 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

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

VecmTransitory(VarxModel varx)

VecmTransitory(VecmTransitory that)
Copy constructor.

VecmTransitory(Vector mu, Matrix pi, Matrix[] gamma, Matrix psi, Matrix sigma)
Construct a transitory VECM(p) model.

Method Summary

static VecmTransitory

fromVarx(VarxModel varx) Construct a transitory VECM(p) from a VARX(p).

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

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 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

VecmTransitory

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

Construct a zero-intercept (mu) transitory 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

VecmTransitory

public VecmTransitory(VarxModel varx)

VecmTransitory

public VecmTransitory(VecmTransitory that)

Copy constructor.

Parameters:

that - a transitory VECM model

Method Detail

fromVarx

public static VecmTransitory fromVarx(VarxModel varx)

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

Returns:

a transitory VECM(p) model