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

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

Direct Known Subclasses:

VecmLongrun, VecmTransitory

public class Vecm
extends java.lang.Object

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

A vector error correction model (VECM(p)) has one the following specifications:

(Transitory):

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

or

(Long-run):

ΔY_t = μ + Π * Y_{t-p} + Σ[Γ_i * Y_{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.

See Also:

• Wikipedia: Error correction model
• Wikipedia: Johansen test
• 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

Vecm(Vecm that)
Copy constructor.

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

Method Summary

int	dimension() Get the dimension of multivariate time series.
ImmutableMatrix	gamma(int i) Get the AR coefficient on the i-th lagged differences.
ImmutableVector	mu() Get the intercept vector.
int	p() Get the order of the VECM model.
ImmutableMatrix	pi() Get the impact matrix.
ImmutableMatrix	psi() Get the coefficients of the deterministic terms.
ImmutableMatrix	sigma() Get the covariance matrix of white noise.

Methods inherited from class java.lang.Object

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

Constructor Detail

Vecm

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

Construct a 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

Vecm

public Vecm(Vecm that)

Copy constructor.

Parameters:

that - a VECM model

Method Detail

mu

public ImmutableVector mu()

Get the intercept vector.

Returns:

the intercept (constant) vector

pi

public ImmutableMatrix pi()

Get the impact matrix.

Returns:

the impact matrix

gamma

public ImmutableMatrix gamma(int i)

Get the AR coefficient on the i-th lagged differences.

Parameters:

i - an index, count from 1

Returns:

the AR coefficient on the i-th lagged differences

psi

public ImmutableMatrix psi()

Get the coefficients of the deterministic terms.

Returns:

the coefficients of the deterministic terms; could be null

sigma

public ImmutableMatrix sigma()

Get the covariance matrix of white noise.

Returns:

the covariance matrix of white noise

dimension

public int dimension()

Get the dimension of multivariate time series.

Returns:

the dimension of multivariate time series

p

public int p()

Get the order of the VECM model.

Returns:

the the order of the VECM model