On sequential estimation of an autoregressive parameter

We study the estimation problem for the first-order autoregressive model The asymptotic behavior of the classical maximum likelihood estimator (MLE) (when the number of observation n tends to infinity) differs essentially between the cases of stable, near stable and explosive models. The main result...

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Bibliographic Details
Published inStochastics and stochastics reports Vol. 60; no. 3-4; pp. 219 - 240
Main Authors Shiryaev, A.N., Spokoiny, V.G.
Format Journal Article
LanguageEnglish
Published Gordon and Breach Science Publishers 01.04.1997
Subjects
1991 Mathematics Subject Classification: 62L12, 62M10
Autoregressive parameter
least square estimator
maximum likelihood estimator
sequential estimation
stopping time
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Summary:We study the estimation problem for the first-order autoregressive model The asymptotic behavior of the classical maximum likelihood estimator (MLE) (when the number of observation n tends to infinity) differs essentially between the cases of stable, near stable and explosive models. The main result of the paper claims the possibility to obtain the universal standard normal limit distribution making use of the random normalizing factor for the divergence where N is a proper stopping time
ISSN:1045-1129
DOI:10.1080/17442509708834107