A machine learning approach to volatility forecasting

TL;DR

This paper assesses how modern machine learning methods perform in forecasting realized variance for DJIA constituents, comparing regularized regressions, tree-based models, and neural networks against HAR-based benchmarks. Using a large, data-rich covariate set and minimal tuning, the authors show that ML methods, particularly random forests and neural networks, generally outperform HAR models, with larger improvements at longer forecast horizons and when extra predictors are included. They diagnose the drivers of ML gains with Accumulated Local Effects (ALE), finding consensus on key volatility predictors but varying importance rankings and evident nonlinear interactions. The study extends to a Value-at-Risk application, where ML maintains an edge, though the gains are more modest, highlighting the practical relevance of ML in risk management. Overall, the work provides a broad benchmark of off-the-shelf ML techniques for volatility forecasting and a roadmap for future improvements via more extensive hyperparameter tuning and model enhancements.

Abstract

We inspect how accurate machine learning (ML) is at forecasting realized variance of the Dow Jones Industrial Average index constituents. We compare several ML algorithms, including regularization, regression trees, and neural networks, to multiple Heterogeneous AutoRegressive (HAR) models. ML is implemented with minimal hyperparameter tuning. In spite of this, ML is competitive and beats the HAR lineage, even when the only predictors are the daily, weekly, and monthly lags of realized variance. The forecast gains are more pronounced at longer horizons. We attribute this to higher persistence in the ML models, which helps to approximate the long-memory of realized variance. ML also excels at locating incremental information about future volatility from additional predictors. Lastly, we propose a ML measure of variable importance based on accumulated local effects. This shows that while there is agreement about the most important predictors, there is disagreement on their ranking, helping to reconcile our results.

Figures (12)

• Figure 1: Illustration of a regression tree.
• Figure 2: Feed-forward neural network.
• Figure 3: Boxplot of cross-sectional out-of-sample relative MSE.
• Figure 4: Inclusion rate in the MCS.
• Figure 5: Forecast accuracy over out-of-sample volatility distribution.