Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-23T13:17:47.095Z Has data issue: false hasContentIssue false
  • English
  • Français

Order estimation by accumulated prediction errors

Published online by Cambridge University Press:  14 July 2016

Jorma Rissanen
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper presents a new criterion based on prediction error which allows the estimation of the number of parameters as well as structures in statistical models. The criterion is valid for short and long samples alike. Unlike Akaike's earlier criterion, also based on prediction error, the criterion proposed here appears to produce consistent error estimates in ARMA processes.

Keywords

ARMA PROCESSESMINIMUM DESCRIPTION LENGTHMODEL COSTPARAMETERSCONSISTENCY
Type
Part 1—Structure and General Methods for Time Series
Information
Journal of Applied Probability , Volume 23 , Issue A: Essays in Time Series and Allied Processes , 1986 , pp. 55 - 61
Copyright
Copyright © 1986 Applied Probability Trust 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Akaike, H. (1974) A new look at the statistical model identification. IEEE Trans. Automatic Control AC-19, 716–723.Google Scholar
Davisson, L. D. (1965) The prediction error of stationary Gaussian time series of unknown covariance. IEEE Trans. Inf. Theory IT-11, 527–532.Google Scholar
Fuller, W. A. and Hasza, D. P. (1981) Properties of predictors for autoregressive time series. J. Amer. Statist. Assoc. 76, 155–161.Google Scholar
Geisser, S. and Eddy, W. (1979) A predictive approach to model selection. J. Amer. Statist. Assoc. 74, 153–160.Google Scholar
Hannan, E. J. (1980) The estimation of the order of an ARMA process. Ann. Statist. 8, 1071–1081.Google Scholar
Hannan, E. J. and Quinn, B. G. (1979) The determination of the order of an autoregression. J. R. Statist. Soc. B 41, 190–195.Google Scholar
Ljung, L. and Caines, P. (1979) Asymptotic normality of prediction error estimators for approximate system models. Stochastics 3, 29–46.Google Scholar
Rissanen, J. (1978) Modeling by shortest data description. Automatica 14, 465–471.CrossRefGoogle Scholar
Rissanen, J. (1980) Consistent order estimates of autoregressive processes by shortest description of data. In Analysis and Optimisation of Stochastic Systems , ed. Jacobs, O., Davis, M., Dempster, M., Harris, C., Parks, P., Academic Press, New York.Google Scholar
Rissanen, J. (1983a) A universal prior for integers and estimation by minimum description lengths. Ann. Statist. 11, 416–431.CrossRefGoogle Scholar
Rissanen, J. (1983b) Estimation of structure by minimum description length. Circuits, Systems, and Signal Processing (Special Issue on Rational Approximations) 1, 395–406.Google Scholar
Rissanen, J. (1984) Universal coding information, prediction, and estimation. IEEE Trans. Inf. Theory IT-30, 629–636.Google Scholar
Rissanen, J. (1985) Minimum description length principle. In Encyclopaedia of Statistical Sciences , Vol. 5, ed. Kotz, S. and Johnson, N. L. Wiley, New York.Google Scholar
Shibata, R. (1976) Selection of the order of an autoregressive model by Akaike's information criterion. Ann. Statist. 63, 117–126.Google Scholar
Shibata, R. (1980) Asymptotically efficient selection of the order of the model for estimating parameters of a linear process. Ann. Statist. 8, 147–164.Google Scholar
Stone, M. (1977) An asymptotic equivalence of choice of model by cross-validation and Akaike's criterion J. R. Statist. Soc. B 39, 44–47.Google Scholar