Annals of Statistics

Explicit representation of finite predictor coefficients and its applications

Akihiko Inoue and Yukio Kasahara

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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

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

First available in Project Euclid: 27 June 2006

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Zentralblatt MATH identifier

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]

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


Inoue, Akihiko; Kasahara, Yukio. Explicit representation of finite predictor coefficients and its applications. Ann. Statist. 34 (2006), no. 2, 973--993. doi:10.1214/009053606000000209.

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