Online Ensemble Learning for Sector Rotation: A Gradient-Free Framework

Abstract

We propose a gradient-free online ensemble learning algorithm that dynamically combines forecasts from a heterogeneous set of machine learning models based on their recent predictive performance, measured by out-of-sample R-squared. The ensemble is model-agnostic, requires no gradient access, and is designed for sequential forecasting under nonstationarity. It adaptively reweights 16 constituent models-three linear benchmarks (OLS, PCR, LASSO) and thirteen nonlinear learners including Random Forests, Gradient-Boosted Trees, and a hierarchy of neural networks (NN1-NN12). We apply the framework to sector rotation, using sector-level features aggregated from firm characteristics. Empirically, sector returns are more predictable and stable than individual asset returns, making them suitable for cross-sectional forecasting. The algorithm constructs sector-specific ensembles that assign adaptive weights in a rolling-window fashion, guided by forecast accuracy. Our key theoretical result bounds the online forecast regret directly in terms of realized out-of-sample R-squared, providing an interpretable guarantee that the ensemble performs nearly as well as the best model in hindsight. Empirically, the ensemble consistently outperforms individual models, equal-weighted averages, and traditional offline ensembles, delivering higher predictive accuracy, stronger risk-adjusted returns, and robustness across macroeconomic regimes, including during the COVID-19 crisis.