Geodesic
Consistency of the maximum likelihood estimate for non-homogeneous Markov–switching models
Ailliot, Pierre1  ; Pène, Françoise2
1 Universitéde Brest, UMR 6205, 29019 Brest, France
2 Université de Brest and IUF, UMR 6205, 29019 Brest, France
ESAIM: Probability and Statistics, Tome 19 (2015), pp. 268-292

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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.

Reçu le :
DOI : 10.1051/ps/2014024
Classification : 62F12, 62M05
Keywords: Markov-switching autoregressive process, non-homogeneous hidden Markov process, maximum likelihood, consistency, stability, lynx data

Ailliot, Pierre 1 ; Pène, Françoise 2

1 Universitéde Brest, UMR 6205, 29019 Brest, France
2 Université de Brest and IUF, UMR 6205, 29019 Brest, France 
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     title = {Consistency of the maximum likelihood estimate for non-homogeneous {Markov{\textendash}switching} models},
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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

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