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Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2013, Number 5(25), Pages 12–25 (Mi vtgu343)  

MATHEMATICS

On the sequential estimation of parameters in a continuous autoregression model

T. V. Emel'yanovaa, V. V. Konevb

a Tomsk State University
b Tomsk State University

Abstract: In this paper, we propose a sequential procedure for estimating unknown parameters for a stable autoregressive continuous time processes. The procedure uses a special rule to stop observations and is based on the classical least squares (LS) estimates but, in contrast, provides control for the mean-square accuracy of estimates. Formulas for the asymptotic duration of observations with an increase in the mean-square accuracy of estimates are obtained. The results can be applied in a wide range of problems such as system identification, adaptive forecasting, and estimation of parameters of spectra of continuous time Gaussian processes.

Keywords: fixed-accuracy estimation, autoregressive process, gaussian process with rational density, sequential estimation, stopping time.

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Document Type: Article
UDC: 519.216.3
Received: 24.06.2013

Citation: T. V. Emel'yanova, V. V. Konev, “On the sequential estimation of parameters in a continuous autoregression model”, Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2013, no. 5(25), 12–25

Citation in format AMSBIB
\Bibitem{EmeKon13}
\by T.~V.~Emel'yanova, V.~V.~Konev
\paper On the sequential estimation of parameters in a~continuous autoregression model
\jour Vestn. Tomsk. Gos. Univ. Mat. Mekh.
\yr 2013
\issue 5(25)
\pages 12--25
\mathnet{http://mi.mathnet.ru/vtgu343}


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  • Вестник Томского государственного университета. Математика и механика
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