Class MultivariateForecastOneStep


  • public class MultivariateForecastOneStep
    extends Object
    The innovation algorithm is an efficient way to obtain a one step least square linear predictor for a multivariate linear time series with known auto-covariance and these properties (not limited to ARMA processes):
    • {xt} can be non-stationary.
    • E(xt) = 0 for all t.
    See Also:
    • "P. J. Brockwell and R. A. Davis, "Proposition. 5.2.2. Chapter 5. Prediction of Stationary Processes," in Time Series: Theory and Methods, Springer, 2006."
    • "P. J. Brockwell and R. A. Davis, "Proposition. 11.4.2. Chapter 11.4 Best Linear Predictors of Second Order Random Vectors," in Time Series: Theory and Methods, Springer, 2006."
    • Constructor Detail

      • MultivariateForecastOneStep

        public MultivariateForecastOneStep​(MultivariateIntTimeTimeSeries Xt,
                                           MultivariateAutoCovarianceFunction K)
        Construct an instance of InnovationAlgorithm for a multivariate time series with known auto-covariance structure.
        Parameters:
        Xt - an m-dimensional time series, length t
        K - auto-covariance function K(i, j) = E(Xi * Xj'), a m x m matrix
    • 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