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Bayesian Forecasting of Dynamic Extreme Quantiles

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  • Douglas E. Johnston

    (Farmingdale State College, The State University of New York, Farmingdale, NY 11735, USA)

Abstract

In this paper, we provide a novel Bayesian solution to forecasting extreme quantile thresholds that are dynamic in nature. This is an important problem in many fields of study including climatology, structural engineering, and finance. We utilize results from extreme value theory to provide the backdrop for developing a state-space model for the unknown parameters of the observed time-series. To solve for the requisite probability densities, we derive a Rao-Blackwellized particle filter and, most importantly, a computationally efficient, recursive solution. Using the filter, the predictive distribution of future observations, conditioned on the past data, is forecast at each time-step and used to compute extreme quantile levels. We illustrate the improvement in forecasting ability, versus traditional methods, using simulations and also apply our technique to financial market data.

Suggested Citation

  • Douglas E. Johnston, 2021. "Bayesian Forecasting of Dynamic Extreme Quantiles," Forecasting, MDPI, vol. 3(4), pages 1-12, October.
  • Handle: RePEc:gam:jforec:v:3:y:2021:i:4:p:45-740:d:653862
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    References listed on IDEAS

    as
    1. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 69-87, January.
    2. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 1994. "Bayesian Analysis of Stochastic Volatility Models: Comments: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 413-417, October.
    3. Mao, Guangyu & Zhang, Zhengjun, 2018. "Stochastic tail index model for high frequency financial data with Bayesian analysis," Journal of Econometrics, Elsevier, vol. 205(2), pages 470-487.
    4. Paul J. Northrop & Nicolas Attalides & Philip Jonathan, 2017. "Cross-validatory extreme value threshold selection and uncertainty with application to ocean storm severity," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(1), pages 93-120, January.
    Full references (including those not matched with items on IDEAS)

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