Data/hora: 07/06/2024 18:02:28

Biblioteca(s): | Embrapa Pantanal.
Data corrente: | 31/05/1996
Data da última atualização: | 31/05/1996
Autoria: | AKAIKE, H.
Título: | Statistical predictor identification.
Ano de publicação: | 1970
Fonte/Imprenta: | Annals of the Institute of Statistics and Mathematics, v.22, n.1, p.203-217, 1970.
Idioma: | Inglês
Conteúdo: | In a recent paper by the present author [1] a simple practical procedure of predictor identification has been proposed. It is the purpose of this paper to provide a theoretical and empirical basis of the procedure. Our procedure is based on a figure of merit of a predictor, which is called the final prediction error (FPE) and is defined as the mean square prediction error of the predictor. We consider the application of the least squares method for the identification of the predictor when the stochastic process under observation is an autoregressive process generated from a strictly stationary and mutually independent innovations. The identification is realized by fitting autoregressive models of successive orders within a prescribed range, computing estimates of FPE for the models, and adopting the one with the minimum of the estimates. The estatistical characteristics of these estimates of FPE and the overall procedure are discussed to show the practical utility of the procedure. A modified of this original procedure is proposed, which shows a consistency, as an estimation procedure of the order of a finite order autoregressive process, which is lacking in the original procedure. The notion of FPE is also applied for the determination of the constants of the decision procedure, which was proposed by T. W. Anderson [2] for the decision of the order of a Gaussian autoregressive process, to provide a third procedure. Performances of the three of procedures, the original one, a modified version and that of Anderson's type, are compared by using various realizations of artificial time series. The results show that for practical applications, where the true orders of autoregressive processes would generally be infinite, the original procedure would be the most useful. Implication of the present identification procedure on the estimation of power spectra will be discussed in a subsequent paper [3]. We shall use the convention of denoting by (u(l)) the column vector of u(l) (l=1,2,..., M) and by v or (v(l,m)) the matrix with (l, m) element v(l, m) (l,m=1,2 ..., M) When the dimension M is of special interest we shall add the subscript M and thus u M and v M are used for the above u and v. The symbol ' will be used to denote the transpose of a matrix or a vector.
Palavras-Chave: | Predictor identification; Preditor; Statistical.
Thesagro: | Estatística; Identificação.
Categoria do assunto: | --
Registro original: | Embrapa Pantanal (CPAP)
Exemplares: | CPAP - (32372-1) - ADC - SP - -- - SP2782 -  - 2782 - DIS