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June 2000 Recursive estimation of a drifted autoregressive parameter
Eduard Belitser
Ann. Statist. 28(3): 860-870 (June 2000). DOI: 10.1214/aos/1015952001


Suppose the $X_0,\dots, X_n$ are observations of a one-dimensional stochastic dynamic process described by autoregression equations when the autoregressive parameter is drifted with time, i.e. it is some function of time: $\theta_0,\dots, \theta_n$, with $\theta_k = \theta(k/n)$. The function $\theta(t)$ is assumed to belong a priori to a predetermined nonparametric class of functions satisfying the Lipschitz smoothness condition. At each time point $t$ those observations are accessible which have been obtained during the preceding time interval. A recursive algorithm is proposed to estimate $\theta(t)$.Under some conditions on the model,we derive the rate of convergence of the proposed estimator when the frequencyof observations $n$ tends to infinity.


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Eduard Belitser. "Recursive estimation of a drifted autoregressive parameter." Ann. Statist. 28 (3) 860 - 870, June 2000.


Published: June 2000
First available in Project Euclid: 12 March 2002

zbMATH: 1105.62373
MathSciNet: MR1792790
Digital Object Identifier: 10.1214/aos/1015952001

Primary: 62G20 , 62M10
Secondary: 60F99

Keywords: autoregressive model , convergence rate , recursive algorithm

Rights: Copyright © 2000 Institute of Mathematical Statistics


Vol.28 • No. 3 • June 2000
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