Optimal window size detection in Value-at-Risk forecasting: A case study on conditional generalised hyperbolic models

Abstract

The conventional parametric approach for financial risk measure estimation involves determining an appropriate quantitative model, as well as a suitable historical sample period in which the model can be trained. While a lion’s share of the existing literature entertains the identification of the most appropriate model for different types of financial assets, or across conflicting market conditions, little is known about the optimal choice of a historical sample period size (or window size) to train the model and estimate model parameters. In this paper, we propose a method to identify an optimal window size for model training when estimating risk measures, such as the widely-utilised Value-at-Risk (VaR) or Expected Shortfall (ES), under the generalised hyperbolic subclasses. We show that the accuracy of VaR estimates may increase significantly through our proposed method of optimal window size detection. In particular, our results demonstrate that, by relaxing the usual restriction of a fixed window size over time, superior VaR forecasts may be produced as a result of improved model parameter estimates.