论文信息 - The Estimation of the Prediction Error Variance

The Estimation of the Prediction Error Variance

Abstract Spectral methods are used to construct an estimate of the variance of the prediction error for a normal, stationary process. The estimate obtained is shown to be strongly consistent and asymptotically normally distributed. Some aspects of the computations with respect to the fast Fourier transform are considered. The latter half of the article consists of a number of simulations, based on both generated and real data, which illustrate the results obtained. The relation between the estimate and that obtained from a high order autoregression is discussed.

E. J. Hannan | E. Hannan | D. F. Nicholls | D. Nicholls

[1] Irene A. Stegun,et al. Handbook of Mathematical Functions. , 1966 .

[2] E. J. Hannan,et al. Multiple time series , 1970 .

[3] P. Moran. The Statistical Analsis of the Canadian Lynx cycle. 1. Structure and Prediction. , 1953 .

[4] Richard H. Jones,et al. Estimation of the Innovation Generalized Variance of a Multivariate Stationary Time Series , 1976 .

[5] P. A. P. Moran,et al. The statistical analysis of the Canadian Lynx cycle. , 1953 .

[6] H. T. Davis,et al. Estimation of the Innovation Variance of a Stationary Time Series , 1968 .

[7] G. Janacek. Estimation of the minimum mean square error of prediction , 1975 .

[8] Richard P. Brent,et al. Algorithm 488: A Gaussian pseudo-random number generator , 1974, Commun. ACM.

[9] H. Akaike. Fitting autoregressive models for prediction , 1969 .

[10] R. Bhansali. Asymptotic Properties of the Wiener‐Kolmogorov Predictor. I , 1974 .

[11] Michel Loève,et al. Probability Theory I , 1977 .