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

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 Details

    • 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 Details

    • 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