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]

This paper develops a simple and computationally efficient parametric approach to the estimation of general hidden Markov models (HMMs). For non-Gaussian HMMs, the computation of the maximum likelihood estimator (MLE) involves a high-dimensional integral that has no analytical solution and can be difficult to approach accurately. We develop a new alternative method based on the theory of estimating functions and deconvolution strategy. Our procedure requires the same assumptions as the MLE and deconvolution estimators. We provide theoretical guarantees on the performance of the resulting estimator; its consistency and asymptotic normality are established. This leads to the construction of confidence intervals. Monte Carlo experiments are investigated and compared with the MLE. Finally, we illustrate our approach on real data for ex-ante interest rate forecasts.

Mots clés: least square estimation; Contrast function; deconvolution; Parametric inference; Stochastic volatility; Measurement error; Contrast func-tion; Expected Inflation; Unobserved components model 1; hidden Markov models; least square esti- mation; parametric inference

Domaines: Statistiques [stat]

Christophe Chesneau, Salima El Kolei, Fabien Navarro. Parametric estimation of hidden Markov models by least squares type estimation and deconvolution. 2020. ⟨hal-01598922v3⟩