Loss Function Sensitivity, Volatility Forecasting, and Dynamic Model Choice: Evidence from Foreign Exchange and Equity Markets

Abstract

This paper examines how volatility model rankings depend on the choice of loss function when the true conditional variance is unobservable and forecast evaluation must rely on noisy volatility proxies. Using daily data for EUR/USD and the S&P 500, it compares GARCH, GJR-GARCH, and EGARCH through rolling one-step-ahead forecasts under four evaluation criteria: MSE, MAE, QLIKE, and joint VaR–ES loss. The results show that model rankings are loss-dependent: EGARCH performs best overall under MSE, QLIKE, and joint VaR–ES loss, whereas GJR-GARCH performs relatively better under MAE. At the same time, model confidence set results indicate that the three models are not sharply distinguishable in finite samples at the 10% level, implying that a superior model set is often more defensible than a unique winner. Dynamic model averaging and dynamic model selection also fail to deliver stable improvements over the best static model in the current sample. The paper contributes by integrating loss-function sensitivity, joint tail-risk evaluation, and dynamic model choice into a unified framework, showing that volatility model comparison is fundamentally conditional on the evaluation criterion, volatility proxy, and market environment.

Author abstract from the research manuscript. Typography and line breaks have been normalized; the linked source may show a different manuscript version.