java.lang.Object
dev.nm.stat.timeseries.linear.multivariate.stationaryprocess.arma.VECM
dev.nm.stat.timeseries.linear.multivariate.stationaryprocess.arma.VECMLongrun

public class VECMLongrun extends VECM
The long-run Vector Error Correction Model (VECM(p)) takes this form. \[ \Delta Y_t = \mu + \Pi Y_{t-p} + \sum \left ( \Gamma_i Y_{t-1} \right ) + \Psi D_t + \epsilon_t, i = 1, 2, ..., p-1 \] 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.

This implementation provides a conversion method between a long-run VECM(p) and a VARX(p) model.

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

    • VECMLongrun

      public VECMLongrun(Vector mu, Matrix pi, Matrix[] gamma, Matrix psi, Matrix sigma)
      Construct a long-run 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
    • VECMLongrun

      public VECMLongrun(Matrix pi, Matrix[] gamma, Matrix psi, Matrix sigma)
      Construct a long-run VECM(p) model with zero-intercept (mu).
      Parameters:
      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
    • VECMLongrun

      public VECMLongrun(VARXModel varx)
      Construct a long-run VECM(p) from a VARX(p).
      Parameters:
      varx - a VARX model
    • VECMLongrun

      public VECMLongrun(VECMLongrun that)
      Copy constructor.
      Parameters:
      that - a long-run VECM model