Combining a Large Pool of Forecasts of Value-at-Risk and Expected Shortfall

TL;DR

This paper explores innovative methods for combining multiple Value-at-Risk and Expected Shortfall forecasts, demonstrating improved accuracy through various statistical and regularisation techniques in an extensive empirical study.

Contribution

It introduces new combining methods for VaR and ES forecasts, including regularisation and interval forecast approaches, and evaluates their performance on a large set of methods.

Findings

Trimmed mean and mixture methods perform well in forecast combination.

Performance-based weighting yields the best results with a diverse set of six methods.

Combining methods improve forecast accuracy compared to individual models.

Abstract

We consider the combination of value-at-risk (VaR) and expected shortfall (ES) forecasts when a large pool of candidate forecasts is available. Given the limited literature in this area, we implement a variety of new combining methods. In terms of simplistic methods, in addition to the mean, we consider the median and mode. As a complement to the previously proposed performance-based weighted combinations, we use regularisation to reduce overfitting in the presence of many weights. Treating VaR and ES forecasts jointly as interval forecasts allows the application of adapted interval forecast combination methods, including trimmed means and a mixtures approach based on inferred probability distributions. In an empirical study involving 90 forecasting methods, trimmed mean combinations, the mixtures method, and performance-based weighting delivered particularly strong results. However, greater forecasting accuracy resulted for a pool of just six methods, chosen to ensure diversity, with performance-based weighting producing the best overall performance.