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A Bayesian model for multiple change point to extremes, with application to environmental and financial data

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  • Fernando Ferraz do Nascimento
  • Wyara Vanesa Moura e Silva

Abstract

Abrupt changes often occur for environmental and financial time series. Most often, these changes are due to human intervention. Change point analysis is a statistical tool used to analyze sudden changes in observations along the time series. In this paper, we propose a Bayesian model for extreme values for environmental and economic datasets that present a typical change point behavior. The model proposed in this paper addresses the situation in which more than one change point can occur in a time series. By analyzing maxima, the distribution of each regime is a generalized extreme value distribution. In this model, the change points are unknown and considered parameters to be estimated. Simulations of extremes with two change points showed that the proposed algorithm can recover the true values of the parameters, in addition to detecting the true change points in different configurations. Also, the number of change points was a problem to be considered, and the Bayesian estimation can correctly identify the correct number of change points for each application. Environmental and financial data were analyzed and results showed the importance of considering the change point in the data and revealed that this change of regime brought about an increase in the return levels, increasing the number of floods in cities around the rivers. Stock market levels showed the necessity of a model with three different regimes.

Suggested Citation

  • Fernando Ferraz do Nascimento & Wyara Vanesa Moura e Silva, 2017. "A Bayesian model for multiple change point to extremes, with application to environmental and financial data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(13), pages 2410-2426, October.
    • Handle: RePEc:taf:japsta:v:44:y:2017:i:13:p:2410-2426
    DOI: 10.1080/02664763.2016.1254733
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    References listed on IDEAS

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    1. Zhongjun Qu & Pierre Perron, 2007. "Estimating and Testing Structural Changes in Multivariate Regressions," Econometrica, Econometric Society, vol. 75(2), pages 459-502, March.
    2. Bradley P. Carlin & Alan E. Gelfand & Adrian F. M. Smith, 1992. "Hierarchical Bayesian Analysis of Changepoint Problems," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(2), pages 389-405, June.
    3. Chib, Siddhartha, 1998. "Estimation and comparison of multiple change-point models," Journal of Econometrics, Elsevier, vol. 86(2), pages 221-241, June.
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