We prove the consistency of the maximum likelihood estimator for a large family of models generalizing the well known Markov-switching AutoRegressive (MS-AR) models by letting the transition probabilities vary in time and depend on covariates. We illustrate our theoretical result on the famous MacKenzie River lynx dataset and on a multi-site model for downscaling rainfall.
DOI : 10.1051/ps/2014024
Mots-clés : Markov-switching autoregressive process, non-homogeneous hidden Markov process, maximum likelihood, consistency, stability, lynx data
@article{PS_2015__19__268_0,
author = {Ailliot, Pierre and P\`ene, Fran\c{c}oise},
title = {Consistency of the maximum likelihood estimate for non-homogeneous {Markov{\textendash}switching} models},
journal = {ESAIM: Probability and Statistics},
pages = {268--292},
publisher = {EDP-Sciences},
volume = {19},
year = {2015},
doi = {10.1051/ps/2014024},
mrnumber = {3412646},
zbl = {1330.62101},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ps/2014024/}
}
TY - JOUR AU - Ailliot, Pierre AU - Pène, Françoise TI - Consistency of the maximum likelihood estimate for non-homogeneous Markov–switching models JO - ESAIM: Probability and Statistics PY - 2015 SP - 268 EP - 292 VL - 19 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ps/2014024/ DO - 10.1051/ps/2014024 LA - en ID - PS_2015__19__268_0 ER -
%0 Journal Article %A Ailliot, Pierre %A Pène, Françoise %T Consistency of the maximum likelihood estimate for non-homogeneous Markov–switching models %J ESAIM: Probability and Statistics %D 2015 %P 268-292 %V 19 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ps/2014024/ %R 10.1051/ps/2014024 %G en %F PS_2015__19__268_0
Ailliot, Pierre; Pène, Françoise. Consistency of the maximum likelihood estimate for non-homogeneous Markov–switching models. ESAIM: Probability and Statistics, Tome 19 (2015), pp. 268-292. doi : 10.1051/ps/2014024. http://archive.numdam.org/articles/10.1051/ps/2014024/
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