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

Christophe Chesneau (), Salima El Kolei () and Fabien Navarro ()
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Christophe Chesneau: Université de Caen - LMNO
Salima El Kolei: CREST - ENSAI
Fabien Navarro: Université Paris 1 Panthéon-Sorbonne - SAMM

Statistical Papers, 2022, vol. 63, issue 5, No 11, 1615-1648

Abstract: Abstract 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 a deconvolution strategy. Our procedure requires the same assumptions as the MLE and deconvolution estimators. We provide theoretical guarantees about 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 using real data for ex-ante interest rate forecasts.

Keywords: Contrast function; Deconvolution; Hidden Markov models; Least square estimation; Parametric inference; 62F12 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s00362-022-01288-x

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