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Asymptotic properties of the maximum likelihood estimator in autoregressive models with Markov regime

Douc, R; Moulines, E and Rydén, Tobias LU (2004) In Annals of Statistics 32(5). p.2254-2304
Abstract
An autoregressive process with Markov regime is an autoregressive process for which the regression function at each time point is given by a nonobservable Markov chain. In this paper we consider the asymptotic properties of the maximum likelihood estimator in a possibly nonstationary process of this kind for which the hidden state space is compact but not necessarily finite. Consistency and asymptotic normality are shown to follow from uniform exponential forgetting of the initial distribution for the hidden Markov chain conditional on the observations.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
autoregressive process, asymptotic normality, consistency, geometric, ergodicity, hidden Markov model, maximum likelihood, identifiability, switching autoregression
in
Annals of Statistics
volume
32
issue
5
pages
2254 - 2304
publisher
Inst Mathematical Statistics
external identifiers
  • wos:000225071400018
  • scopus:21244500381
ISSN
0090-5364
DOI
10.1214/009053604000000021
language
English
LU publication?
yes
id
eec3c358-7710-44cd-8880-73bd077afcdc (old id 261097)
date added to LUP
2007-08-02 12:25:56
date last changed
2017-12-10 04:35:45
@article{eec3c358-7710-44cd-8880-73bd077afcdc,
  abstract     = {An autoregressive process with Markov regime is an autoregressive process for which the regression function at each time point is given by a nonobservable Markov chain. In this paper we consider the asymptotic properties of the maximum likelihood estimator in a possibly nonstationary process of this kind for which the hidden state space is compact but not necessarily finite. Consistency and asymptotic normality are shown to follow from uniform exponential forgetting of the initial distribution for the hidden Markov chain conditional on the observations.},
  author       = {Douc, R and Moulines, E and Rydén, Tobias},
  issn         = {0090-5364},
  keyword      = {autoregressive process,asymptotic normality,consistency,geometric,ergodicity,hidden Markov model,maximum likelihood,identifiability,switching autoregression},
  language     = {eng},
  number       = {5},
  pages        = {2254--2304},
  publisher    = {Inst Mathematical Statistics},
  series       = {Annals of Statistics},
  title        = {Asymptotic properties of the maximum likelihood estimator in autoregressive models with Markov regime},
  url          = {http://dx.doi.org/10.1214/009053604000000021},
  volume       = {32},
  year         = {2004},
}