Modeling and evaluating conditional quantile dynamics in VaR forecasts

Abstract

We focus on the time-varying modeling of VaR at a given coverage $\tau$, assessing whether the quantiles of the distribution of the returns standardized by their conditional means and standard deviations exhibit predictable dynamics. Models are evaluated via simulation, determining the merits of the asymmetric Mean Absolute Deviation as a loss function to rank forecast performances. The empirical application on the Fama-French 25 value-weighted portfolios with a moving forecast window shows substantial improvements in forecasting conditional quantiles by keeping the predicted quantile unchanged unless the empirical frequency of violations falls outside a data-driven interval around $\tau$.