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Maximum likelihood estimates of incorrect Markov models for time series and the derivation of AIC

Published online by Cambridge University Press:  14 July 2016

Yosihiko Ogata
Yosihiko Ogata*
Affiliation:
The Institute of Statistical Mathematics, Tokyo
*
∗ Postal address: The Institute of Statistical Mathematics, 4–6–7 Minami-Azabu, Minato-Ku, Tokyo, Japan.
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Abstract

The asymptotic behavior of the maximum likelihood estimators of Markov models or autoregressive models are given when the true distribution is not a member of the assumed parametric family. The derivation of Akaike's Information Criterion is reviewed for this case.

Keywords

AICAUTOREGRESSIVE MODELERGODIC STATIONARY PROCESSMAXIMAL CORRELATION COEFFICIENTMAXIMUM LIKELIHOOD ESTIMATORNEGATIVE ENTROPY

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 17 , Issue 1 , March 1980 , pp. 59 - 72
Copyright
Copyright © Applied Probability Trust 1980 

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