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Some applications of nonlinear and non-Gaussian state--space modelling by means of hidden Markov models

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  • Roland Langrock

Abstract

Nonlinear and non-Gaussian state--space models (SSMs) are fitted to different types of time series. The applications include homogeneous and seasonal time series, in particular earthquake counts, polio counts, rainfall occurrence data, glacial varve data and daily returns on a share. The considered SSMs comprise Poisson, Bernoulli, gamma and Student- t distributions at the observation level. Parameter estimations for the SSMs are carried out using a likelihood approximation that is obtained after discretization of the state space. The approximation can be made arbitrarily accurate, and the approximated likelihood is precisely that of a finite-state hidden Markov model (HMM). The proposed method enables us to apply standard HMM techniques. It is easy to implement and can be extended to all kinds of SSMs in a straightforward manner.

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  • Roland Langrock, 2011. "Some applications of nonlinear and non-Gaussian state--space modelling by means of hidden Markov models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(12), pages 2955-2970, March.
    • Handle: RePEc:taf:japsta:v:38:y:2011:i:12:p:2955-2970
    DOI: 10.1080/02664763.2011.573543
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    1. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178, Decembrie.
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    1. Carlos A. Abanto-Valle & Gabriel Rodríguez & Hernán B. Garrafa-Aragón, 2020. "Stochastic Volatility in Mean: Empirical Evidence from Stock Latin American Markets," Documentos de Trabajo / Working Papers 2020-481, Departamento de Economía - Pontificia Universidad Católica del Perú.
    2. Johan Dahlin & Thomas B. Schon, 2015. "Getting Started with Particle Metropolis-Hastings for Inference in Nonlinear Dynamical Models," Papers 1511.01707, arXiv.org, revised Mar 2019.
    3. Roland Langrock & Théo Michelot & Alexander Sohn & Thomas Kneib, 2015. "Semiparametric stochastic volatility modelling using penalized splines," Computational Statistics, Springer, vol. 30(2), pages 517-537, June.
    4. Michels, Rouven & Ötting, Marius & Langrock, Roland, 2023. "Bettors’ reaction to match dynamics: Evidence from in-game betting," European Journal of Operational Research, Elsevier, vol. 310(3), pages 1118-1127.
    5. Iain L. MacDonald, 2021. "Is EM really necessary here? Examples where it seems simpler not to use EM," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(4), pages 629-647, December.
    6. Carlos A. Abanto‐Valle & Roland Langrock & Ming‐Hui Chen & Michel V. Cardoso, 2017. "Maximum likelihood estimation for stochastic volatility in mean models with heavy‐tailed distributions," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 33(4), pages 394-408, August.

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