Class 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 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