Functional Data-Driven Quantile Model Averaging with Application to Cryptocurrencies

Abstract

Given the high volatility and susceptibility to extreme events in the cryptocurrency market, forecasting tail risk is of paramount importance. Value-at-Risk (VaR), a quantile-based risk measure, is widely used for assessing tail risk and is central to monitoring financial market stability. In data-rich environments, functional data from various domains are employed to forecast conditional quantiles. However, the infinite-dimensional nature of functional data introduces uncertainty. This paper addresses this uncertainty problem by proposing a novel data-driven conditional quantile model averaging (MA) approach. With a set of candidate models varying by the number of components, MA assigns weights to each model determined by a K-fold cross-validation criterion. We prove the asymptotic optimality of the selected weights in terms of minimizing the excess final prediction error when all candidate models are misspecified. Additionally, when the true regression relationship belongs to the set of candidate models, we provide consistency results for the averaged estimators. Numerical studies indicate that, in most cases, the proposed method outperforms other model selection and averaging methods, particularly for extreme quantiles in cryptocurrency markets.