Class MultivariateInnovationAlgorithm


  • public class MultivariateInnovationAlgorithm
    extends Object
    This class implements the part of the innovation algorithm that computes the prediction error covariances, V and prediction coefficients Θ. The coefficients depend only on the auto-covariance function and time horizon, not on any particular time series data.
    See Also:
    • "P. J. Brockwell and R. A. Davis, "Proposition 5.2.2, Chapter 5, Multivariate Time Series," 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," Time Series: Theory and Methods, Springer, 2006."
    • Constructor Detail

      • MultivariateInnovationAlgorithm

        public MultivariateInnovationAlgorithm​(int T,
                                               MultivariateAutoCovarianceFunction K)
        Run the Innovation Algorithm to compute the prediction parameters, V and Θ.
        Parameters:
        T - time series length
        K - the covariance structure of the time series
    • Method Detail

      • theta

        public ImmutableMatrix theta​(int i,
                                     int j)
        Get the coefficients of the linear predictor.
        Parameters:
        i - i, ranging from 0 to T
        j - j, ranging from 0 to T
        Returns:
        Θ[i][j]; Θ[?][0] = 1
      • covariance

        public ImmutableMatrix covariance​(int n)
        Get the covariance matrix for prediction errors at time t for x^t+1.
        Parameters:
        n - time, ranging from 0 to t, the end of observation time
        Returns:
        the covariance matrix for prediction errors at time n