Value-at-risk forecasting via dynamic asymmetric exponential power distributions

In the value-at-risk (VaR) literature, many existing works assume that the noise distribution is the same over time. To take into account the potential time-varying dynamics of stock returns, we propose a dynamic asymmetric exponential distribution-based framework. The new method includes a time-varying shape parameter to control the dynamic shape of the distribution, a time-varying probability parameter to control the dynamic proportion of positive returns, and a time-varying scale parameter to control the dynamic volatility. We combine the generalized method of moments and the exponentially weighted moving average (EWMA) approach to derive specifications for these time-varying parameters. Empirical applications demonstrate the superior performance of the proposed method when compared with various GARCH and EWMA approaches without time variation in the innovations.