Class ConditionalSumOfSquares

  • All Implemented Interfaces:
    ARMAFit

    public class ConditionalSumOfSquares
    extends Object
    implements ARMAFit
    The method Conditional Sum of Squares (CSS) fits an ARIMA model by minimizing the conditional sum of squares. The CSS estimates are conditional on the assumption that the past unobserved errors are 0s. The estimation produced by CSS can be used as a starting point for a better algorithm, e.g., the maximum likelihood. Note that the order of integration is taken as an input, not estimated. The R equivalent function is arima.
    • Constructor Detail

      • ConditionalSumOfSquares

        public ConditionalSumOfSquares​(double[] x,
                                       int p,
                                       int d,
                                       int q,
                                       int maxIterations)
        Fit an ARIMA model for the observations using CSS. Note that the algorithm fits only an ARMA model. d is taken as an input. If the differenced input time series is not zero-mean, it is first de-mean-ed before running the algorithm as in Brockwell and Davis. When reporting the model, we compute the intercept to match the mean.
        Parameters:
        x - the time series of observations
        p - the number of AR terms
        d - the order of integration
        q - the number of MA terms
        maxIterations - the maximum number of iterations
      • ConditionalSumOfSquares

        public ConditionalSumOfSquares​(double[] x,
                                       int p,
                                       int d,
                                       int q)
        Fit an ARIMA model for the observations using CSS. Note that the algorithm fits only an ARMA model. d is taken as an input. If the differenced input time series is not zero-mean, it is first de-mean-ed before running the algorithm as in Brockwell and Davis. When reporting the model, we compute the intercept to match the mean.
        Parameters:
        x - the time series of observations
        p - the number of AR terms
        d - the order of integration
        q - the number of MA terms
    • Method Detail

      • nParams

        public int nParams()
        Get the number of parameters for the estimation/fitting. They are the AR terms, MA terms, and variance (sigma^2).
        Returns:
        the number of parameters
      • getModel

        public ARIMAModel getModel()
        Get the fitted ARIMA model.
        Specified by:
        getModel in interface ARMAFit
        Returns:
        the fitted ARIMA model
      • getARMAModel

        public ARMAModel getARMAModel()
        Get the fitted ARMA model.
        Returns:
        the fitted ARMA model
      • var

        public double var()
        Description copied from interface: ARMAFit
        Get the variance of the white noise.
        Specified by:
        var in interface ARMAFit
        Returns:
        σ2
      • covariance

        public Matrix covariance()
        Get the asymptotic covariance matrix of the estimated parameters, φ and θ. The estimators are asymptotically normal.
        Specified by:
        covariance in interface ARMAFit
        Returns:
        the asymptotic covariance matrix
      • stderr

        public ImmutableVector stderr()
        Get the asymptotic standard errors of the estimated parameters, φ and θ. The estimators are asymptotically normal.
        Specified by:
        stderr in interface ARMAFit
        Returns:
        the asymptotic errors
      • AICC

        public double AICC()
        Compute the AICC, a model selection criterion.
        Specified by:
        AICC in interface ARMAFit
        Returns:
        the AICC