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Bayesian Forecasting of Dynamic Extreme Quantiles

Farmingdale State College, The State University of New York, Farmingdale, NY 11735, USA
Academic Editor: Sonia Leva
Received: 1 September 2021 / Revised: 1 October 2021 / Accepted: 7 October 2021 / Published: 11 October 2021
(This article belongs to the Special Issue Bayesian Time Series Forecasting)
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. View Full-Text
Keywords: extreme value theory; quantile forecasting; particle filter; risk-management; value-at-risk extreme value theory; quantile forecasting; particle filter; risk-management; value-at-risk
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MDPI and ACS Style

Johnston, D.E. Bayesian Forecasting of Dynamic Extreme Quantiles. Forecasting 2021, 3, 729-740. https://0-doi-org.brum.beds.ac.uk/10.3390/forecast3040045

AMA Style

Johnston DE. Bayesian Forecasting of Dynamic Extreme Quantiles. Forecasting. 2021; 3(4):729-740. https://0-doi-org.brum.beds.ac.uk/10.3390/forecast3040045

Chicago/Turabian Style

Johnston, Douglas E. 2021. "Bayesian Forecasting of Dynamic Extreme Quantiles" Forecasting 3, no. 4: 729-740. https://0-doi-org.brum.beds.ac.uk/10.3390/forecast3040045

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