Open Access
April 2006 Explicit representation of finite predictor coefficients and its applications
Akihiko Inoue, Yukio Kasahara
Ann. Statist. 34(2): 973-993 (April 2006). DOI: 10.1214/009053606000000209


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 is based on the alternate applications of projection operators associated with the infinite past and the infinite future. Applying the result to long memory processes, we give the rate of convergence of the finite predictor coefficients and prove an inequality of Baxter-type.


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Akihiko Inoue. Yukio Kasahara. "Explicit representation of finite predictor coefficients and its applications." Ann. Statist. 34 (2) 973 - 993, April 2006.


Published: April 2006
First available in Project Euclid: 27 June 2006

zbMATH: 1098.62120
MathSciNet: MR2283400
Digital Object Identifier: 10.1214/009053606000000209

Primary: 60G25
Secondary: 62M10 , 62M20

Keywords: AR coefficients , Baxter’s inequality , fractional ARIMA processes , long memory , MA coefficients , Predictor

Rights: Copyright © 2006 Institute of Mathematical Statistics

Vol.34 • No. 2 • April 2006
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