The continuous-time hidden Markov model based on discretization. Properties of estimators and applications Gámiz Pérez, María Luz Limnios, Nikolaos Segovia García, María del Carmen Hidden Markov model Poisson process Maximun-likelihood estimation Asymptotic properties This work was jointly supported by the Spanish Ministry of Science and Innovation-State Research Agency through grants numbered PID2020-120217RB-I00 and PID2021-123737NB-I00, and the IMAG-Maria de Maeztu grant CEX2020-001105-/AEI/10.13039/501100011033; and by the Spanish Junta de Andalucia through grant number B-FQM-284-UGR20. In this paper we consider continuous-time hidden Markov processes (CTHMM). The model considered is a two-dimensional stochastic process (Xt, Yt) , with Xt an unobserved (hidden) Markov chain defined by its generating matrix and Yt an observed process whose distribution law depends on Xt and is called the emission function. In general, we allow the process Yt to take values in a subset of the q-dimensional real space, for some q. The coupled process (Xt, Yt) is a continuous-time Markov chain whose generator is constructed from the generating matrix of X and the emission distribution. We study the theoretical properties of this two-dimensional process using a formulation based on semi-Markov processes. Observations of the CTHMM are obtained by discretization considering two different scenarii. In the first case we consider that observations of the process Y are registered regularly in time, while in the second one, observations arrive at random. Maximum-likelihood estimators of the characteristics of the coupled process are obtained in both scenarii and the asymptotic properties of these estimators are shown, such as consistency and normality. To illustrate the model a real-data example and a simulation study are considered. 2023-07-12T09:46:25Z 2023-07-12T09:46:25Z 2023-06-23 journal article Gámiz, M.L., Limnios, N. & Segovia-García, M.C. The continuous-time hidden Markov model based on discretization. Properties of estimators and applications. Stat Inference Stoch Process (2023). [https://doi.org/10.1007/s11203-023-09292-0] https://hdl.handle.net/10481/83624 10.1007/s11203-023-09292-0 eng http://creativecommons.org/licenses/by/4.0/ open access Atribución 4.0 Internacional Springer Nature