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

Class VARMAForecastOneStep

  • public class VARMAForecastOneStep
extends Object
    This is an implementation, adapted for an ARMA process, of the innovation algorithm, which is an efficient way of obtaining a one step least square linear predictor.
    See Also:
    • "P. J. Brockwell and R. A. Davis, "Chapter 5.3, Recursive Prediction of an ARMA(p,q) Process," Time Series: Theory and Methods, Springer, 2006."
    • "P. J. Brockwell and R. A. Davis, "Eqs. 11.4.26, 11.4.27, 11.4.28, Chapter 11.4, Recursive Prediction of an ARMA(p,q) Process, Best Linear Predictors of Second Order Random Vectors," Time Series: Theory and Methods, Springer, 2006."

    • Constructor Detail

      • VARMAForecastOneStep

        public VARMAForecastOneStep​(MultivariateIntTimeTimeSeries Xt,
                            VARMAModel model)
        Construct an instance of InnovationAlgorithm for a multivariate ARMA time series.
        Parameters:
        Xt - an m-dimensional time series
        model - the ARMA model

    • Method Detail

      • xHat

        public ImmutableVector xHat​(int n)
        Get the one-step prediction \(\hat{X}_{n+1} = P_{\mathfrak{S_n}}X_{n+1}\), made at time n.
        Parameters:
        n - time, ranging from 0 to T, the end of observation time
        Returns:
        the one-step prediction \(\hat{X}_{n+1}\)

      • theta

        public ImmutableMatrix theta​(int i,
                             int j)
        Get the coefficients of the linear predictor.
        Parameters:
        i - i, ranging from 1 to t
        j - j, ranging from 1 to t
        Returns:
        Θ[i][j]

      • covariance

        public ImmutableMatrix covariance​(int n)
        Get the covariance matrix for prediction errors for \(\hat{x}_{n+1}\), made at time n.
        Parameters:
        n - time, ranging from 0 to T, the end of observation time
        Returns:
        the covariance matrix for prediction errors at time n