Class InnovationsAlgorithm


  • public class InnovationsAlgorithm
    extends Object
    The innovations algorithm is an efficient way to obtain a one step least square linear predictor for a univariate 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.
    This class implements the part of the innovations algorithm that computes the prediction error variances, v and prediction coefficients θ. The coefficients depend only on the auto-covariance function and time horizon, not on any particular time series data.
    • Constructor Detail

      • InnovationsAlgorithm

        public InnovationsAlgorithm​(int T,
                                    AutoCovarianceFunction K)
        Constructs an instance of InnovationsAlgorithm for a univariate time series with known auto-covariance structure.
        Parameters:
        T - time series length
        K - the auto-covariance function
    • Method Detail

      • theta

        public double theta​(int i,
                            int j)
        Gets 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
      • var

        public double var​(int n)
        Gets the mean squared error for prediction errors at time n for \(\hat{x}_{n+1}\), i.e., \(E(x_{n+1} - \hat{x}_{n+1})^2\).
        Parameters:
        n - time, ranging from 0 to T, the end of observation time
        Returns:
        the mean squared error (variance)