Ergodicity of Autoregressive Processes with Markov-switching and Consistency of the Maximum-likelihood Estimator

Christian Francq; Michel Roussignol

doi:10.1080/02331889808802659

Ergodicity of Autoregressive Processes with Markov-switching and Consistency of the Maximum-likelihood Estimator

Christian Francq
, Michel Roussignol

Research output: Contribution to journal › Article › peer-review

Abstract

An autoregressive model with Markov-switching assumes a sequence of random vectors to be a non linear autoregressive model given a sequence of non observed state variables which forms a Markov chain. A particular case of this model is the hidden Markov model. In this paper conditions for the existence of an ergodic stationary solution are given and consistency of the maximum likelihood estimator is proved.

Original language	English
Pages (from-to)	151-173
Number of pages	23
Journal	Statistics
Volume	32
Issue number	2
DOIs	https://doi.org/10.1080/02331889808802659
Publication status	Published - 1 Jan 1998
Externally published	Yes

Keywords

Consistency
Hidden Markov chain
Maximum likelihood
Non linear time series models
Switching models

Access to Document

10.1080/02331889808802659

Cite this

@article{510acb1cd3cf496bb1c5200595d43999,

title = "Ergodicity of Autoregressive Processes with Markov-switching and Consistency of the Maximum-likelihood Estimator",

abstract = "An autoregressive model with Markov-switching assumes a sequence of random vectors to be a non linear autoregressive model given a sequence of non observed state variables which forms a Markov chain. A particular case of this model is the hidden Markov model. In this paper conditions for the existence of an ergodic stationary solution are given and consistency of the maximum likelihood estimator is proved.",

keywords = "Consistency, Hidden Markov chain, Maximum likelihood, Non linear time series models, Switching models",

author = "Christian Francq and Michel Roussignol",

year = "1998",

month = jan,

day = "1",

doi = "10.1080/02331889808802659",

language = "English",

volume = "32",

pages = "151--173",

journal = "Statistics",

issn = "0233-1888",

number = "2",

}

TY - JOUR

T1 - Ergodicity of Autoregressive Processes with Markov-switching and Consistency of the Maximum-likelihood Estimator

AU - Francq, Christian

AU - Roussignol, Michel

PY - 1998/1/1

Y1 - 1998/1/1

N2 - An autoregressive model with Markov-switching assumes a sequence of random vectors to be a non linear autoregressive model given a sequence of non observed state variables which forms a Markov chain. A particular case of this model is the hidden Markov model. In this paper conditions for the existence of an ergodic stationary solution are given and consistency of the maximum likelihood estimator is proved.

AB - An autoregressive model with Markov-switching assumes a sequence of random vectors to be a non linear autoregressive model given a sequence of non observed state variables which forms a Markov chain. A particular case of this model is the hidden Markov model. In this paper conditions for the existence of an ergodic stationary solution are given and consistency of the maximum likelihood estimator is proved.

KW - Consistency

KW - Hidden Markov chain

KW - Maximum likelihood

KW - Non linear time series models

KW - Switching models

U2 - 10.1080/02331889808802659

DO - 10.1080/02331889808802659

M3 - Article

AN - SCOPUS:11744382461

SN - 0233-1888

VL - 32

SP - 151

EP - 173

JO - Statistics

JF - Statistics

IS - 2

ER -

Ergodicity of Autoregressive Processes with Markov-switching and Consistency of the Maximum-likelihood Estimator

Abstract

Keywords

Access to Document

Fingerprint

Cite this