# SuanShu, a Java numerical and statistical library

com.numericalmethod.suanshu.stats.timeseries.linear.multivariate.stationaryprocess.arma

## Class VECM

• java.lang.Object
• com.numericalmethod.suanshu.stats.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: $\Delta Y_t = \mu + \Pi Y_{t-p} + \sum \left ( \Gamma_i Y_{t-1} \right ) + \Psi D_t + \epsilon_t, i = 1, 2, ..., p-1$ Yt, μ and εt are n-dimensional vectors. The impact matrix Π and the coefficients i} of the lagged time series are n-by-n matrices; Dt 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.

• 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 and Description
VECM(VECM that)
Copy constructor.
VECM(Vector mu, Matrix pi, Matrix[] gamma, Matrix psi, Matrix sigma)
Construct a VECM(p) model.
• ### Method Summary

All Methods
Modifier and Type Method and 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