Does Machine Learning Beat the GARCH Benchmark? Historical, Filtered, and Neural Tail-Risk Measures Across Thirty-Nine Global Equity Markets

Abstract

We compare three families of Value-at-Risk and expected shortfall estimators—rolling historical simulation, GARCH(1,1) filtered historical simulation (FHS), and a walk-forward multi-quantile LSTM—on identical, strictly out-of-sample footing across thirty-nine developed, emerging, and frontier equity markets over 2005–2025 (192,789 market-days). The answer to the title question is no. Historical simulation fails the Christoffersen independence test in every market. Filtering repairs most of this: FHS passes conditional coverage in nineteen markets, attains a 4.9% breach rate against a 5% target, and prices expected shortfall essentially without bias (mean Acerbi–Székely Z2 of −0.003). The neural measure improves on historical simulation but passes conditional coverage in only four markets and understates tail severity by roughly 20% (Z2 = −0.195); it tracks filtered more closely than historical VaR (within-market correlation 0.53 versus 0.40, p < 0.001), which indicates that much of the neural signal is volatility filtering in disguise. Quadrupling the network narrows this gap without closing it. In the macroeconomic panel, however, the neural family is the least procyclical: a one-point rise in GDP growth compresses historical tail risk by 4.3% but neural risk by only 1.5%. Machine learning tail-risk measures should therefore be benchmarked against filtered, not merely unconditional, classical methods and used alongside rather than instead of them.