Abstract
Markov-switching models are attractive for analysing time series that exhibit different stochastic processes along different periods, and where the regime-switching is controlled by an unobservable Markovian process. Model flexibility can be enhanced considering regime-specific distributions, whose distributional parameters may be modelled using smooth functions of covariates. Here, we propose a two-state Markov-switching model using full Bayesian inference and accounting for extreme value modelling. The proposal is illustrated by analysing energy prices.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Adam, T., Mayr, A., Kneib, T.: Gradient boosting in Markov-switching generalized additive models for location, scale, and shape. Econom. Stat. 22, 3–16 (2022). https://doi.org/10.1016/j.ecosta.2021.04.002
Feldmann, C.C., Mews, S., Langrock, R.: Modelling time-of-day variation in hidden Markov models using cyclyc P-splines. In Bergherr, E., Groll, A., and Mayr, A. (eds.): Proceedings of the 37th International Workshop of Statistical Modelling, pp. 131–134. TU Dortmund University, Dortmund, Germany (2023). https://iwsm2023.statistik.tu-dortmund.de/storages/iwsm2023-statistik/r/dokumente/IWSM_2023_Conference_Proceedings.pdf
Hamilton, J.D.: Regime switching models. In: Durlauf, S.N., and Blume, L.E. (eds.) Macroeconometrics and Time Series Analysis. The New Palgrave Economics Collection, pp. 202–209. Palgrave Macmillan, London, UK (2010). https://doi.org/10.1057/9780230280830_23
Langrock, R., Kneib, T., Glennie, R., Michelot, T.: Markov-switching generalized additive models. Stat. Comput. 27(1), 259–270 (2017). https://doi.org/10.1007/s11222-015-9620-3
Laurini, F., Pauli, F.: Smoothing sample extremes: the mixed model approach. Comput. Stat. Data Anal. 53(11), 3842–3854 (2009). https://doi.org/10.1016/j.csda.2009.04.005
Sanchez-Espigares, J.A., Lopez-Moreno A.: MSwM: fitting Markov switching models. R package version 1.5 (2021). https://CRAN.R-project.org/package=MSwM
Shaby, B.A., Reich, B.J., Cooley, D., Kaufman, C.G.: A Markov-switching model for heat waves. Ann. Appl. Stat. 10(1), 74–93 (2016). https://doi.org/10.1214/15-AOAS873
Umlauf, N., Klein, N., Zeileis, A.: BAMLSS: Bayesian additive models for location, scale, and shape (and beyond). J. Comput. Graph. Stat. 27(3), 612–627 (2018). https://doi.org/10.1080/10618600.2017.1407325
Vehtari, A., Gelman, A., Gabry, J.: Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Stat. Comput. 27(5), 1413–1432 (2017). https://doi.org/10.1007/s11222-016-9696-4
Xu, S.G., Reich, B.J.: Bayesian nonparametric quantile process regression and estimation of marginal quantile effects. Biom. 79(1), 151–164 (2023). https://doi.org/10.1111/biom.13576
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Gioia, V., Di Credico, G., Pauli, F. (2024). A Bayesian Markov-Switching for Smooth Modelling of Extreme Value Distributions. In: Einbeck, J., Maeng, H., Ogundimu, E., Perrakis, K. (eds) Developments in Statistical Modelling. IWSM 2024. Contributions to Statistics. Springer, Cham. https://doi.org/10.1007/978-3-031-65723-8_10
Download citation
DOI: https://doi.org/10.1007/978-3-031-65723-8_10
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-65722-1
Online ISBN: 978-3-031-65723-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)