Application of Novel Exponential (Semi-)Parametric Short and Long Memory GARCH Models under Regulatory Requirements of Basel III

This paper evaluates the forecasting performance of an expanded class of (semi-)parametric GARCH models belonging to the EGARCH family (EGF), including recently introduced long and short memory specifications and their semiparametric extensions. The semiparametric variants employ a multiplicative volatility decomposition into conditional and slowly varying unconditional components, where the latter is estimated via a data-driven local polynomial smoother to accommodate non-stationarities commonly observed in financial time series. Based on the revised Basel Committee framework for market-risk assessment, all models are capable of producing rolling one-day-ahead forecasts for Value at Risk (VaR) and Expected Shortfall (ES) under a wide range of symmetric and skewed innovation distributions. Their forecasting accuracy is examined using the regulatory traffic light tests for VaR and the recently developed ES-specific traffic light procedure, complemented by the regulatory loss function. In addition, model selection incorporates both a recently proposed corrected firm-oriented loss function that accounts for opportunity costs and the Weighted Absolute Deviation (WAD) criterion. The empirical comparison demonstrates that (semiparametric) long memory GARCH models - particularly those combining fractional dynamics with nonparametric scale adjustments - can serve as valuable alternatives to traditional parametric short memory models, offering more stable volatility estimates and improved tail-risk forecasts for practical risk management applications.