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

Class VECM

java.lang.Object

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

Direct Known Subclasses:

VECMLongrun, VECMTransitory

public class VECM
extends Object

A Vector Error Correction Model (VECM(p)) has one of the following specifications:

Transitory: \[ \Delta Y_t = \mu + \Pi Y_{t-1} + \sum \left ( \Gamma_i Y_{t-1} \right ) + \Psi D_t + \epsilon_t, i = 1, 2, ..., p-1 \] or

Long-run: \[ \Delta Y_t = \mu + \Pi Y_{t-p} + \sum \left ( \Gamma_i Y_{t-1} \right ) + \Psi D_t + \epsilon_t, i = 1, 2, ..., p-1 \] 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.

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

Method Summary

Modifier and Type	Method	Description
int	dimension()	Get the dimension of the multivariate time series.
ImmutableMatrix[]	gamma()	Get the AR coefficients of the lagged differences; null if p = 1
ImmutableMatrix	gamma(int i)	Get the AR coefficient of 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 white noise covariance matrix.

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 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

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 of the i-th lagged differences.

Parameters:

i - an index, counting from 1

Returns:

the AR coefficient of the i-th lagged differences

gamma

public ImmutableMatrix[] gamma()

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

Returns:

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

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 white noise covariance matrix.

Returns:

the white noise covariance matrix

dimension

public int dimension()

Get the dimension of the multivariate time series.

Returns:

the dimension of the multivariate time series

p

public int p()

Get the order of the VECM model.

Returns:

the order of the VECM model