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 Probl. Peredachi Inf., 1999, Volume 35, Issue 2, Pages 75–82 (Mi ppi444)

Large Systems

Nonstationary Time Series with a Close Alternative Hypothesis: Locally Asymptotic Distribution of the Likelihood Ratio

P. Boulongne, K. A. Ol'shanskii, V. I. Piterbarg

Abstract: Within the framework of the autoregressive model, we solve the problem of testing the hypothesis of the existence of the unit root of the characteristic polynomial against a close alternative hypothesis of this root to come infinitesimally close to unity. The asymptotic distribution of the likelihood ratio is calculated. This distribution is found to be substantially dependent on the information amount of the innovation noise distribution.

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English version:
Problems of Information Transmission, 1999, 35:2, 158–165

Bibliographic databases:
UDC: 621.391.1:519.27

Citation: P. Boulongne, K. A. Ol'shanskii, V. I. Piterbarg, “Nonstationary Time Series with a Close Alternative Hypothesis: Locally Asymptotic Distribution of the Likelihood Ratio”, Probl. Peredachi Inf., 35:2 (1999), 75–82; Problems Inform. Transmission, 35:2 (1999), 158–165

Citation in format AMSBIB
\Bibitem{BouOlsPit99} \by P.~Boulongne, K.~A.~Ol'shanskii, V.~I.~Piterbarg \paper Nonstationary Time Series with a~Close Alternative Hypothesis: Locally Asymptotic Distribution of the Likelihood Ratio \jour Probl. Peredachi Inf. \yr 1999 \vol 35 \issue 2 \pages 75--82 \mathnet{http://mi.mathnet.ru/ppi444} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1728909} \zmath{https://zbmath.org/?q=an:0946.62082} \transl \jour Problems Inform. Transmission \yr 1999 \vol 35 \issue 2 \pages 158--165 

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This publication is cited in the following articles:
1. O. V. Gaas, “On the Asymptotical Power of the Likelihood Ratio Criterion for Testing the Hypothesis of Nonstationarity of an Autoregressive Series with Cauchy Innovations”, Problems Inform. Transmission, 40:2 (2004), 175–185
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