The choice of GARCH models to forecast value-at-risk for currencies (euro exchange rates), crypto assets (Bitcoin and Ethereum), gold, silver and crude oil: Automated processes, statistical distribution models and the specification of the mean equation

Regular or automated processes require reliable software applications that provide accurate volatility and Value-at-Risk forecasts. The univariate and multivariate GARCH models proposed in the literature are reviewed and the suitability of selected R functions for automated forecasting systems is discussed. With the Markov-switching GARCH function constructed for modelling regime changes, parameter estimates are reliably obtained in studies with moving time windows. In contrast, in the case of structural breaks or outliers, the algorithm of the ordinary GARCH function often does not return valid parameter estimates and fails. VaR prognoses are produced for extreme quantiles (up to 99.9%) and three alternative distribution assumptions (Skew Student-T, Student-T and Gaussian). Accurate one-day-ahead VaR predictions up to the 99% quantile are generally obtained for the time series when Skew Student-T distributed innovations are assumed. The VaR exceedance rates and their percentage deviations from the target alpha as well as the mean and median excess loss are reported. The accompanying mean equation is often omitted when fitting GARCH models to heteroskedastic time series. The impact of this on the accuracy of VaR forecasts is investigated. Coefficients of the ordinary (Pearson) and the default correlation are calculated for moving time windows. Since the calculated default correlation depends on the VaR forecasts, analyses are performed for different quantiles, the ordinary and the MS-GARCH function and specifications of mean equations.