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

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 di...

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Bibliographic Details
Published in:Statistical papers (Berlin, Germany) Germany), 2022-10, Vol.63 (5), p.1615-1648
Main Authors: Chesneau, Christophe, El Kolei, Salima, Navarro, Fabien
Format: Article
Language:English
Subjects:
Confidence intervals
Deconvolution
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Exact solutions
Finance
Insurance
Interest rates
Management
Markov analysis
Markov chains
Mathematics and Statistics
Maximum likelihood estimators
Methods
Normality
Operations Research/Decision Theory
Parameter estimation
Probability Theory and Stochastic Processes
Random variables
Regular Article
Statistics
Statistics for Business
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Summary: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.
ISSN:0932-5026
1613-9798
DOI:10.1007/s00362-022-01288-x