MATHEMATICS

On the sequential estimation of parameters in a continuous autoregression model

T. V. Emel'yanova^a, V. V. Konev<sup>b

a</sup> 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.

UDC: 519.216.3

Received: 24.06.2013