Asymptotic properties of the maximum likelihood estimator in autoregressive models with Markov regime
(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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/261097
- author
- Douc, R ; Moulines, E and Rydén, Tobias LU
- organization
- publishing date
- 2004
- 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
- Institute of 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
- 2016-04-01 16:42:08
- date last changed
- 2022-04-15 06:27:32
@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}},
keywords = {{autoregressive process; asymptotic normality; consistency; geometric; ergodicity; hidden Markov model; maximum likelihood; identifiability; switching autoregression}},
language = {{eng}},
number = {{5}},
pages = {{2254--2304}},
publisher = {{Institute of 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}},
doi = {{10.1214/009053604000000021}},
volume = {{32}},
year = {{2004}},
}