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Hidden semi-Markov-switching quantile regression for time series

Author

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  • Maruotti, Antonello
  • Petrella, Lea
  • Sposito, Luca

Abstract

A hidden semi-Markov-switching quantile regression model is introduced as an extension of the hidden Markov-switching one. The proposed model allows for arbitrary sojourn-time distributions in the states of the Markov-switching chain. Parameters estimation is carried out via maximum likelihood estimation method using the Asymmetric Laplace distribution. As a by product of the model specification, the formulae and methods for forecasting, the state prediction, decoding and model checking that exist for ordinary hidden Markov-switching models can be applied to the proposed model. A simulation study to investigate the behaviour of the proposed model is performed covering several experimental settings. The empirical analysis studies the relationship between the stock index from the emerging market of China and those from the advanced markets, and investigates the determinants of high levels of pollution in an Italian small city.

Suggested Citation

  • Maruotti, Antonello & Petrella, Lea & Sposito, Luca, 2021. "Hidden semi-Markov-switching quantile regression for time series," Computational Statistics & Data Analysis, Elsevier, vol. 159(C).
    • Handle: RePEc:eee:csdana:v:159:y:2021:i:c:s0167947321000426
    DOI: 10.1016/j.csda.2021.107208
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    1. Bulla, Jan & Bulla, Ingo, 2006. "Stylized facts of financial time series and hidden semi-Markov models," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2192-2209, December.
    2. Liu Xiaochun & Luger Richard, 2018. "Markov-switching quantile autoregression: a Gibbs sampling approach," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 22(2), pages 1, April.
    3. Bartolucci, Francesco & Farcomeni, Alessio, 2009. "A Multivariate Extension of the Dynamic Logit Model for Longitudinal Data Based on a Latent Markov Heterogeneity Structure," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 816-831.
    4. Xiao, Zhijie, 2009. "Quantile cointegrating regression," Journal of Econometrics, Elsevier, vol. 150(2), pages 248-260, June.
    5. Andrew Ang & Allan Timmermann, 2012. "Regime Changes and Financial Markets," Annual Review of Financial Economics, Annual Reviews, vol. 4(1), pages 313-337, October.
    6. Bernardi, Mauro & Maruotti, Antonello & Petrella, Lea, 2012. "Skew mixture models for loss distributions: A Bayesian approach," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 617-623.
    7. Ye, Wuyi & Zhu, Yangguang & Wu, Yuehua & Miao, Baiqi, 2016. "Markov regime-switching quantile regression models and financial contagion detection," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 21-26.
    8. Francesco Lagona & Antonello Maruotti & Fabio Padovano, 2015. "Multilevel multivariate modelling of legislative count data, with a hidden Markov chain," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 178(3), pages 705-723, June.
    9. Roland Langrock & Timo Adam & Vianey Leos‐Barajas & Sina Mews & David L. Miller & Yannis P. Papastamatiou, 2018. "Spline‐based nonparametric inference in general state‐switching models," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 72(3), pages 179-200, August.
    10. Punzo, Antonio & Bagnato, Luca & Maruotti, Antonello, 2018. "Compound unimodal distributions for insurance losses," Insurance: Mathematics and Economics, Elsevier, vol. 81(C), pages 95-107.
    11. Yu, Keming & Moyeed, Rana A., 2001. "Bayesian quantile regression," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 437-447, October.
    12. Paolo Frumento & Matteo Bottai, 2016. "Parametric modeling of quantile regression coefficient functions," Biometrics, The International Biometric Society, vol. 72(1), pages 74-84, March.
    13. Merlo, Luca & Petrella, Lea & Raponi, Valentina, 2020. "Sectoral Decomposition of CO2 World Emissions: A Joint Quantile Regression Approach," International Review of Environmental and Resource Economics, now publishers, vol. 14(2-3), pages 197-239, October.
    14. Francesco Bartolucci & Alessio Farcomeni, 2010. "A note on the mixture transition distribution and hidden Markov models," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(2), pages 132-138, March.
    15. Jennifer Pohle & Roland Langrock & Floris M. Beest & Niels Martin Schmidt, 2017. "Selecting the Number of States in Hidden Markov Models: Pragmatic Solutions Illustrated Using Animal Movement," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 22(3), pages 270-293, September.
    16. Tobias Rydén & Timo Teräsvirta & Stefan Åsbrink, 1998. "Stylized facts of daily return series and the hidden Markov model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(3), pages 217-244.
    17. Bulla, Jan, 2006. "Application of Hidden Markov Models and Hidden Semi-Markov Models to Financial Time Series," MPRA Paper 7675, University Library of Munich, Germany.
    18. Dunmur, A. P. & Titterington, D. M., 1998. "The influence of initial conditions on maximum likelihood estimation of the parameters of a binary hidden Markov model," Statistics & Probability Letters, Elsevier, vol. 40(1), pages 67-73, September.
    19. Miljkovic, Tatjana & Grün, Bettina, 2016. "Modeling loss data using mixtures of distributions," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 387-396.
    20. Maria Marino & Marco Alfó, 2015. "Latent drop-out based transitions in linear quantile hidden Markov models for longitudinal responses with attrition," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 9(4), pages 483-502, December.
    21. Park E.S. & Guttorp P. & Henry R.C., 2001. "Multivariate Receptor Modeling for Temporally Correlated Data by Using MCMC," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1171-1183, December.
    22. Antonello Maruotti & Antonio Punzo & Luca Bagnato, 2019. "Hidden Markov and Semi-Markov Models with Multivariate Leptokurtic-Normal Components for Robust Modeling of Daily Returns Series," Journal of Financial Econometrics, Oxford University Press, vol. 17(1), pages 91-117.
    23. Bulla, Jan & Bulla, Ingo & Nenadic, Oleg, 2010. "hsmm -- An R package for analyzing hidden semi-Markov models," Computational Statistics & Data Analysis, Elsevier, vol. 54(3), pages 611-619, March.
    24. Langrock, R. & Zucchini, W., 2011. "Hidden Markov models with arbitrary state dwell-time distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 715-724, January.
    25. Jan Bulla & Andreas Berzel, 2008. "Computational issues in parameter estimation for stationary hidden Markov models," Computational Statistics, Springer, vol. 23(1), pages 1-18, January.
    26. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    27. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    28. Antonello Maruotti & Antonio Punzo, 2021. "Initialization of Hidden Markov and Semi‐Markov Models: A Critical Evaluation of Several Strategies," International Statistical Review, International Statistical Institute, vol. 89(3), pages 447-480, December.
    29. J. Hambuckers & T. Kneib & R. Langrock & A. Silbersdorff, 2018. "A Markov-switching generalized additive model for compound Poisson processes, with applications to operational loss models," Quantitative Finance, Taylor & Francis Journals, vol. 18(10), pages 1679-1698, October.
    30. Wu, Qiang & Yao, Weixin, 2016. "Mixtures of quantile regressions," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 162-176.
    31. Maria Marino & Alessio Farcomeni, 2015. "Linear quantile regression models for longitudinal experiments: an overview," METRON, Springer;Sapienza Università di Roma, vol. 73(2), pages 229-247, August.
    32. Iain L. MacDonald, 2014. "Numerical Maximisation of Likelihood: A Neglected Alternative to EM?," International Statistical Review, International Statistical Institute, vol. 82(2), pages 296-308, August.
    33. Inmaculada Martinez‐Zarzoso & Antonello Maruotti, 2013. "The environmental Kuznets curve: functional form, time‐varying heterogeneity and outliers in a panel setting," Environmetrics, John Wiley & Sons, Ltd., vol. 24(7), pages 461-475, November.
    34. Petrella, Lea & Raponi, Valentina, 2019. "Joint estimation of conditional quantiles in multivariate linear regression models with an application to financial distress," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 70-84.
    35. R. A. Rigby & D. M. Stasinopoulos, 2005. "Generalized additive models for location, scale and shape," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(3), pages 507-554, June.
    36. Bernardi, Mauro & Bottone, Marco & Petrella, Lea, 2018. "Bayesian quantile regression using the skew exponential power distribution," Computational Statistics & Data Analysis, Elsevier, vol. 126(C), pages 92-111.
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