Package dev.nm.stat.timeseries.linear.multivariate.stationaryprocess.arma

Class VARMAModel

  • Direct Known Subclasses:
    VARModel, VMAModel
    public class VARMAModel
extends VARIMAModel
    A multivariate ARMA model, Xt, takes this form. \[ X_t = \mu + \Sigma \phi_i X_{t-i} + \Sigma \theta_j \epsilon_{t-j} + \epsilon_t, \]
    See Also:

    • Constructor Detail

      • VARMAModel

        public VARMAModel​(Vector mu,
                  Matrix[] phi,
                  Matrix[] theta,
                  Matrix sigma)
        Construct a multivariate ARMA model.
        Parameters:
        mu - the intercept (constant) vector
        phi - the AR coefficients (excluding the initial 1); null if no AR coefficient
        theta - the MA coefficients (excluding the initial 1); null if no MA coefficient
        sigma - the white noise covariance matrix

      • VARMAModel

        public VARMAModel​(Vector mu,
                  Matrix[] phi,
                  Matrix[] theta)
        Construct a multivariate ARMA model with unit variance.
        Parameters:
        mu - the intercept (constant) vector
        phi - the AR coefficients (excluding the initial 1); null if no AR coefficient
        theta - the MA coefficients (excluding the initial 1); null if no MA coefficient

      • VARMAModel

        public VARMAModel​(Matrix[] phi,
                  Matrix[] theta,
                  Matrix sigma)
        Construct a multivariate ARMA model with zero-intercept (mu).
        Parameters:
        phi - the AR coefficients (excluding the initial 1); null if no AR coefficient
        theta - the MA coefficients (excluding the initial 1); null if no MA coefficient
        sigma - the white noise covariance matrix

      • VARMAModel

        public VARMAModel​(Matrix[] phi,
                  Matrix[] theta)
        Construct a multivariate ARMA model with unit variance and zero-intercept (mu).
        Parameters:
        phi - the AR coefficients (excluding the initial 1); null if no AR coefficient
        theta - the MA coefficients (excluding the initial 1); null if no MA coefficient

      • VARMAModel

        public VARMAModel​(ARMAModel model)
        Construct a multivariate model from a univariate ARMA model.
        Parameters:
        model - a univariate ARMA model

      • VARMAModel

        public VARMAModel​(VARMAModel that)
        Copy constructor.
        Parameters:
        that - a multivariate ARMA model

    • Method Detail

      • conditionalMean

        public Vector conditionalMean​(Matrix arLags,
                              Matrix maLags)
        Compute the multivariate ARMA conditional mean, given all the lags.
        Parameters:
        arLags - the AR lags
        maLags - the MA lags
        Returns:
        the conditional mean

      • unconditionalMean

        public Vector unconditionalMean()
        Compute the multivariate ARMA unconditional mean.
        Returns:
        the unconditional mean

      • getDemeanedModel

        public VARMAModel getDemeanedModel()
        Get the demeaned version of the time series model. \[ Y_t = (X_t - \mu) = \sum_{i=1}^p \phi_i (X_{t-i} - \mu) + \sum_{i=1}^q \theta_j \epsilon_{t-j} + \epsilon_t \] μ is the unconditional mean.
        Returns:
        the demeaned time series