Non parametric observation-driven hidden Markov model

Hanna Bacave, Pierre-Olivier Cheptou, Nikolaos Limnios and Nathalie Peyrard

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 14, 4366-4395

Abstract: Hidden Markov models (HMM) are used in different fields to study the dynamics of a process that cannot be directly observed. However, in some cases, the structure of dependencies of a HMM is too simple to describe the dynamics of the hidden process. In particular, in some applications in finance and in ecology, the transition probabilities of the hidden Markov chain can also depend on the current observation. In this work, we are interested in extending the classical HMM to this situation. We refer to the extended model as the observation-driven hidden Markov model (OD-HMM). We present a complete study of the general non parametric OD-HMM with discrete and finite state spaces. We study its identifiability and the consistency of the maximum likelihood estimators. We derive the associated forward-backward equations for the E-step of the EM algorithm. The quality of the procedure is tested on simulated datasets. We illustrate the use of the model on an application focused on the study of annual plant dynamics. This work establishes theoretical and practical foundations for this framework that could be further extended to the parametric context in order to simplify estimation and to hidden semi-Markov models for more realism.

Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/03610926.2024.2419899 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:lstaxx:v:54:y:2025:i:14:p:4366-4395

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/lsta20

DOI: 10.1080/03610926.2024.2419899

Access Statistics for this article

Communications in Statistics - Theory and Methods is currently edited by Debbie Iscoe

More articles in Communications in Statistics - Theory and Methods from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().