Penalized estimation of flexible hidden Markov models for time series of counts

DOI10.48550/ARXIV.1901.03275zbMATH Open1427.62091arXiv1901.03275OpenAlexW2962680222WikidataQ127650397 ScholiaQ127650397MaRDI QIDQ145607

Christian H. Weiß, Roland Langrock, Timo Adam, Timo Adam, Christian H. Weiß, Roland Langrock

Publication date: 10 January 2019

Published in: Metron (Search for Journal in Brave)

Abstract: Hidden Markov models are versatile tools for modeling sequential observations, where it is assumed that a hidden state process selects which of finitely many distributions generates any given observation. Specifically for time series of counts, the Poisson family often provides a natural choice for the state-dependent distributions, though more flexible distributions such as the negative binomial or distributions with a bounded range can also be used. However, in practice, choosing an adequate class of (parametric) distributions is often anything but straightforward, and an inadequate choice can have severe negative consequences on the model's predictive performance, on state classification, and generally on inference related to the system considered. To address this issue, we propose an effectively nonparametric approach to fitting hidden Markov models to time series of counts, where the state-dependent distributions are estimated in a completely data-driven way without the need to select a distributional family. To avoid overfitting, we add a roughness penalty based on higher-order differences between adjacent count probabilities to the likelihood, which is demonstrated to produce smooth probability mass functions of the state-dependent distributions. The feasibility of the suggested approach is assessed in a simulation experiment, and illustrated in two real-data applications, where we model the distribution of i) major earthquake counts and ii) acceleration counts of an oceanic whitetip shark (Carcharhinus longimanus) over time.

Full work available at URL: https://arxiv.org/abs/1901.03275

zbMATH Keywords

count datastate-space modelnonparametric statisticspenalized likelihoodearthquaketime series modelingsmoothing parameter selection

Mathematics Subject Classification ID

Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10) Applications of statistics to biology and medical sciences; meta analysis (62P10) Applications of statistics to environmental and related topics (62P12) Nonparametric estimation (62G05) Markov processes: estimation; hidden Markov models (62M05) Seismology (including tsunami modeling), earthquakes (86A15)

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Related Items (8)

Estimation of steady-state quantities of an HMM with some rarely generated emissions ⋮ Flexible estimation of the state dwell-time distribution in hidden semi-Markov models ⋮ Quantile hidden semi-Markov models for multivariate time series ⋮ Semiparametric estimation of INAR models using roughness penalization ⋮ Hhsmm: An R package for hidden hybrid Markov/semi-Markov models ⋮ Guest editor's introduction to the special issue on ``Hidden Markov models: theory and applications ⋮ A regularized hidden Markov model for analyzing the `hot shoe' in football ⋮ countHMM

Uses Software

• R
• CRAN
• hmm.discnp

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