Bayesian Forecasting of Dynamic Extreme Quantiles
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 back...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-10-01
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| Series: | Forecasting |
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| Online Access: | https://www.mdpi.com/2571-9394/3/4/45 |
| _version_ | 1827672390873645056 |
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| author | Douglas E. Johnston |
| author_facet | Douglas E. Johnston |
| author_sort | Douglas E. Johnston |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T04:07:42Z |
| format | Article |
| id | doaj.art-e443e7dbe37848d3b8a55cb08bbc14c9 |
| institution | Directory Open Access Journal |
| issn | 2571-9394 |
| language | English |
| last_indexed | 2024-03-10T04:07:42Z |
| publishDate | 2021-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Forecasting |
| spelling | doaj.art-e443e7dbe37848d3b8a55cb08bbc14c92023-11-23T08:19:44ZengMDPI AGForecasting2571-93942021-10-013472974010.3390/forecast3040045Bayesian Forecasting of Dynamic Extreme QuantilesDouglas E. Johnston0Farmingdale State College, The State University of New York, Farmingdale, NY 11735, USAIn 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.https://www.mdpi.com/2571-9394/3/4/45extreme value theoryquantile forecastingparticle filterrisk-managementvalue-at-risk |
| spellingShingle | Douglas E. Johnston Bayesian Forecasting of Dynamic Extreme Quantiles Forecasting extreme value theory quantile forecasting particle filter risk-management value-at-risk |
| title | Bayesian Forecasting of Dynamic Extreme Quantiles |
| title_full | Bayesian Forecasting of Dynamic Extreme Quantiles |
| title_fullStr | Bayesian Forecasting of Dynamic Extreme Quantiles |
| title_full_unstemmed | Bayesian Forecasting of Dynamic Extreme Quantiles |
| title_short | Bayesian Forecasting of Dynamic Extreme Quantiles |
| title_sort | bayesian forecasting of dynamic extreme quantiles |
| topic | extreme value theory quantile forecasting particle filter risk-management value-at-risk |
| url | https://www.mdpi.com/2571-9394/3/4/45 |
| work_keys_str_mv | AT douglasejohnston bayesianforecastingofdynamicextremequantiles |