Class VARXModel


  • public class VARXModel
    extends VARMAXModel
    A VARX (Vector AutoRegressive model with eXogeneous inputs) model, Xt, takes this form. \[ Y_t = \mu + \Sigma \phi_i * Y_{t-i} + \Psi * D_t + \epsilon_t \] where Yt, μ and εt are n-dimensional vectors. The n-by-n matrices i} (i = 1, 2, ..., p) denote the AR coefficients. 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 an n-by-m matrix ψ.

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

    See Also:
    • "S. Johansen, "ch. 2-4, pp. 11-88," Likelihood-Based Inference in Cointegrated Vector Autoregressive Models, Oxford, Oxford University Press, 1995."
    • "S. Johansen and K. Juselius, Maximum Likelihood Estimation and Inference on Cointegration - with Applications to the Demand for Money, Oxford Bull. of Econ. and Stat, vol. 52, 169-210, 1990."
    • Constructor Detail

      • VARXModel

        public VARXModel​(Vector mu,
                         Matrix[] phi,
                         Matrix psi,
                         Matrix sigma)
        Construct a VARX model.
        Parameters:
        mu - the intercept (constant) vector
        phi - the AR coefficients (excluding the initial 1)
        psi - the coefficients of the deterministic terms (excluding the intercept)
        sigma - the white noise covariance matrix
      • VARXModel

        public VARXModel​(Vector mu,
                         Matrix[] phi,
                         Matrix psi)
        Construct a VARX model with unit variance.
        Parameters:
        mu - the intercept (constant) vector
        phi - the AR coefficients (excluding the initial 1)
        psi - the coefficients of the deterministic terms (excluding the intercept)
      • VARXModel

        public VARXModel​(Matrix[] phi,
                         Matrix psi,
                         Matrix sigma)
        Construct a VARX model with zero-mean.
        Parameters:
        phi - the AR coefficients (excluding the initial 1)
        psi - the coefficients of the deterministic terms (excluding the intercept)
        sigma - the white noise covariance matrix
      • VARXModel

        public VARXModel​(Matrix[] phi,
                         Matrix psi)
        Construct a VARX model with unit variance and zero-mean.
        Parameters:
        phi - the AR coefficients (excluding the initial 1)
        psi - the coefficients of the deterministic terms (excluding the intercept)
      • VARXModel

        public VARXModel​(VECMTransitory vecm)
        Construct a VARX(p) from a transitory VECM(p).
        Parameters:
        vecm - a transitory VECM(p)
      • VARXModel

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

        public VARXModel​(VARXModel that)
        Copy constructor.
        Parameters:
        that - a VARX model