Equity Volatility Forecasting: ML vs. Econometric Models

Deep Dive

Summer 2026 research project, supervised by Emily Marshall and Tyler Wake (Denison Economics), revisiting Hansen & Lunde's (2005) "Does anything beat a GARCH(1,1)?" for equities: does machine learning add genuine forecasting skill over parametric and naive benchmarks, does any statistical edge translate into portfolio economic value, and how much does that answer depend on the loss function and strategy used to evaluate it.

Eleven models across four families — three GARCH variants (GARCH, EGARCH, GJR-GARCH), two HAR-RV specifications (Corsi's original plus a VIX-augmented HAR-X), a deliberately naive persistence floor, three machine learning models (Random Forest, XGBoost, LSTM), and two GARCH-ML hybrids — are evaluated across 18 U.S. equities using an expanding-window walk-forward split (trained on 2010–2017, tested on 2018–2025, 96 monthly refits per model-asset pair).

At the 1-day horizon under squared-error loss, no model beats the naive persistence forecast (Diebold-Mariano p<0.001 against every alternative); a 90%-confidence Model Confidence Set retains only Persistence, HAR-RV, and HAR-X. Switching to QLIKE loss inverts the ranking, with XGBoost and its GARCH-hybrid emerging as the only survivors instead — a reminder that a single loss function can make or break an "ML beats GARCH" headline.

Economic evaluation is more consistent: Volatility-Timing and Risk-Parity strategies underperform passive benchmarks under all eleven models (a monthly rebalance needs 20-day accuracy, where the 1-day-winning HAR and persistence models are actually among the weakest performers), while Regime-Based and Variance-Risk-Premium (VRP) strategies outperform under all eleven — VRP's best result (Sharpe up to 2.96) comes from GJR-GARCH(1,1) at near-zero compute cost, far cheaper than the LSTM's 24-hour walk-forward for a comparable gain.

Project complete pending final faculty sign-off. Full manuscript and symposium poster linked below.