Geodesic
On the sequential estimation of parameters in a~continuous autoregression model
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 5 (2013), pp. 12-25

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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. 
@article{VTGU_2013_5_a1,
     author = {T. V. Emel'yanova and V. V. Konev},
     title = {On the sequential estimation of parameters in a~continuous autoregression model},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {12--25},
     publisher = {mathdoc},
     number = {5},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2013_5_a1/}
}
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T. V. Emel'yanova; V. V. Konev. On the sequential estimation of parameters in a~continuous autoregression model. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 5 (2013), pp. 12-25. http://geodesic.mathdoc.fr/item/VTGU_2013_5_a1/