Parametric estimation of hidden Markov models by least squares type estimation and deconvolution

Christophe Chesneau (1) , Salima El Kolei (2) , Fabien Navarro (2)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme
2 CREST - Centre de Recherche en Economie et Statistique [Bruz]

In this paper, we study a specific hidden Markov chain defined by the equation: $Y_i=X_i+\varepsilon_i$, $i=1,\ldots,n+1$, where $(X_i)_{i \geq 1}$ is a real-valued stationary Markov chain and $(\varepsilon_i)_{i \geq 1}$ is a noise independent of $(X_i)_{i\geq 1}$. We develop a new parametric approach obtained by minimization of a particular contrast taking advantage of the regressive problem and based on deconvolution strategy. We provide theoretical guarantees on the performance of the resulting estimator; its consistency and its asymptotic normality are established.

Mots clés: Contrast function; deconvolution; least square estimation; parametric inference; stochastic volatility

Domaines: Statistiques [stat]

Christophe Chesneau, Salima El Kolei, Fabien Navarro. Parametric estimation of hidden Markov models by least squares type estimation and deconvolution. 2017. ⟨hal-01598922v1⟩