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January, 1978 Linear Prediction by Autoregressive Model Fitting in the Time Domain
R. J. Bhansali
Ann. Statist. 6(1): 224-231 (January, 1978). DOI: 10.1214/aos/1176344081


Let $\{x_t\}$ be a purely nondeterministic stationary process satisfying all the assumptions made by Berk (1974), and $\{y_t\}$ be another purely nondeterministic stationary process. Assume that $y_t$ is independent of $x_t$ but has exactly the same statistical properties as that of $x_t$. Consider the linear prediction of future values of $y_t$ on the basis of past values, using prediction constants estimated from a realisation of $T$ observations of $x_t$ by least-squares fitting of an autoregression of order $k$. By assuming that $k \rightarrow \infty, k^3/T \rightarrow 0$ as $T \rightarrow \infty$, the effect on the mean square error of prediction of estimating the autoregressive coefficients is determined. This effect is the same as for the case when the prediction constants are estimated by factorising a "windowed" estimate of the spectral density function of $x_t$.


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R. J. Bhansali. "Linear Prediction by Autoregressive Model Fitting in the Time Domain." Ann. Statist. 6 (1) 224 - 231, January, 1978.


Published: January, 1978
First available in Project Euclid: 12 April 2007

zbMATH: 0383.62061
MathSciNet: MR461824
Digital Object Identifier: 10.1214/aos/1176344081

Primary: 62M20
Secondary: 62M10

Keywords: autoregressive process , time domain , time series , Yule-Walker equations

Rights: Copyright © 1978 Institute of Mathematical Statistics


Vol.6 • No. 1 • January, 1978
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