The Annals of Statistics

Explicit representation of finite predictor coefficients and its applications

Akihiko Inoue and Yukio Kasahara

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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 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.

Article information

Source
Ann. Statist. Volume 34, Number 2 (2006), 973-993.

Dates
First available: 27 June 2006

Permanent link to this document
http://projecteuclid.org/euclid.aos/1151418248

Digital Object Identifier
doi:10.1214/009053606000000209

Mathematical Reviews number (MathSciNet)
MR2283400

Zentralblatt MATH identifier
1098.62120

Subjects
Primary: 60G25: Prediction theory [See also 62M20]
Secondary: 62M20: Prediction [See also 60G25]; filtering [See also 60G35, 93E10, 93E11] 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]

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

Citation

Inoue, Akihiko; Kasahara, Yukio. Explicit representation of finite predictor coefficients and its applications. The Annals of Statistics 34 (2006), no. 2, 973--993. doi:10.1214/009053606000000209. http://projecteuclid.org/euclid.aos/1151418248.


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