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

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 R². 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 - Ordinary Least Squares (OLS), Principal Component Regression (PCR), and LASSO - and thirteen nonlinear machine learning models, including Random Forests, Gradient-Boosted Regression Trees, and a hierarchy of feedforward neural networks (NN1-NN12). We apply this framework to the sector rotation problem, using sector-level features derived by aggregating firm-specific characteristics. Empirically, we find that sector-level returns are more predictable and stable than individual asset returns, making them well-suited for cross-sectional forecasting. To exploit this structure, our algorithm constructs sector-specific ensembles that assign adaptive weights to constituent models in a rolling-window fashion, guided by their forecast accuracy. Our key theoretical contribution is to bound the online forecast regret directly in terms of realized out-of-sample R², a standard empirical performance metric that here serves as the loss function in the ensemble procedure. This provides a novel and interpretable guarantee: the ensemble performs nearly as well as the best model in hindsight in terms of predictive power. Empirical results show that the ensemble consistently outperforms individual models, equal-weighted combinations, and traditional offline ensemble methods in both predictive accuracy and economic value. When used to construct sector rotation portfolios, it delivers substantial improvements in risk-adjusted returns, maintains robustness across macroeconomic regimes, and demonstrates resilience during periods of financial stress, including the COVID-19 crisis.