Dept. Math, Hokkaido Univ. EPrints Server

Explicit representation of finite predictor coefficients and its applications

Preprint Series # 646
Inoue, Akihiko and Kasahara, Yukio Explicit representation of finite predictor coefficients and its applications. (2004);

[img]PDF - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
238Kb

Abstract

We consider the finite-past predictor coefficients of stationary time series, and establish an explicit representation for them, in terms of the MA and AR coefficients. The proof involves the alternate iteration of projection operators associated with the infinite past and the infinite future. We provide several applications, which include rates of convergence of the finite predictor coefficients, an equality of Baxter-type for long memory processes, and a simple representation of the partial autocorrelation function (PACF). We use the last result to obtain the precise asymptotic behavior of PACF with remainder, for the fractional ARIMA processes.

Item Type:Preprint
Uncontrolled Keywords:Predictior coefficients, AR coefficients, MA coefficients, prediction, fractional ARIMA processes, long memory, Baxter's inequality, partial autocorrelation functions
Subjects:60-xx PROBABILITY THEORY AND STOCHASTIC PROCESSES
ID Code:186