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Time-varying extreme pattern with dynamic models

Author

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  • Fernando Nascimento
  • Dani Gamerman
  • Hedibert Lopes

Abstract

This paper is concerned with the analysis of time series data with time-varying extreme pattern. This is achieved via a model formulation that considers separately the central part and the tail of the distributions, using a two-component mixture model. Extremes beyond a threshold are assumed to follow a generalized Pareto distribution (GPD). Temporal dependence is induced by allowing the GPD parameters to vary with time. Temporal variation and dependence is introduced at a latent level via the novel use of dynamic linear models (DLM). Novelty lies in the time variation of the shape and scale parameter of the resulting distribution. These changes in limiting regimes as time changes reflect better the data behavior, with important gains in estimation and interpretation. The central part follows a nonparametric mixture approach. The uncertainty about the threshold is explicitly considered. Posterior inference is performed through Markov Chain Monte Carlo (MCMC) methods. A variety of scenarios can be entertained and include the possibility of alternation of presence and absence of a finite upper limit of the distribution for different time periods. Simulations are carried out in order to analyze the performance of our proposed model. We also apply the proposed model to financial time series: returns of Petrobrás stocks and SP500 index. Results show advantage of our proposal over currently entertained models such as stochastic volatility, with improved estimation of high quantiles and extremes. Copyright Sociedad de Estadística e Investigación Operativa 2016

Suggested Citation

  • Fernando Nascimento & Dani Gamerman & Hedibert Lopes, 2016. "Time-varying extreme pattern with dynamic models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 131-149, March.
    • Handle: RePEc:spr:testjl:v:25:y:2016:i:1:p:131-149
    DOI: 10.1007/s11749-015-0444-4
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    References listed on IDEAS

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    1. Carvalho, Carlos M. & Lopes, Hedibert F., 2007. "Simulation-based sequential analysis of Markov switching stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4526-4542, May.
    2. Zhao, Xin & Scarrott, Carl John & Oxley, Les & Reale, Marco, 2011. "GARCH dependence in extreme value models with Bayesian inference," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(7), pages 1430-1440.
    3. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    4. Emma F. Eastoe & Jonathan A. Tawn, 2009. "Modelling non‐stationary extremes with application to surface level ozone," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 58(1), pages 25-45, February.
    5. MacDonald, A. & Scarrott, C.J. & Lee, D. & Darlow, B. & Reale, M. & Russell, G., 2011. "A flexible extreme value mixture model," Computational Statistics & Data Analysis, Elsevier, vol. 55(6), pages 2137-2157, June.
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    Cited by:

    1. Jue Tao Lim & Yiting Han & Borame Sue Lee Dickens & Lee Ching Ng & Alex R Cook, 2020. "Time varying methods to infer extremes in dengue transmission dynamics," PLOS Computational Biology, Public Library of Science, vol. 16(10), pages 1-19, October.
    2. Chiara Lattanzi & Manuele Leonelli, 2019. "A changepoint approach for the identification of financial extreme regimes," Papers 1902.09205, arXiv.org.
    3. Marcelo Bourguignon & Fernando Ferraz Nascimento, 2021. "Regression models for exceedance data: a new approach," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 157-173, March.

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