The Nonstationarity-Complexity Tradeoff in Return Prediction

Abstract

We investigate machine learning models for stock return prediction in non-stationary environments, revealing a fundamental nonstationarity-complexity tradeoff : complex models reduce misspecification error but require longer training windows that introduce stronger nonstationarity. We resolve this tension with a novel model selection method that jointly optimizes model class and training window size using a tournament procedure that adaptively evaluates candidates on non-stationary validation data. Our theoretical analysis demonstrates that this approach balances misspecification error, estimation variance, and non-stationarity, performing close to the best model in hindsight. Applying our method to 17 industry portfolio returns, we consistently outperform standard rolling-window benchmarks, improving out-of-sample R 2 by 14-23% on average. During NBER-designated recessions, improvements are substantial: our method achieves positive R^2 during the Gulf War recession while benchmarks are negative, and improves R^2 in absolute terms by at least 80 bps during the 2001 recession as well as superior performance during the 2008 Financial Crisis. Economically, a trading strategy based on our selected model generates 31% higher cumulative returns averaged across the industries.

Keywords: Non-Stationarity, Model Complexity, Return Prediction, Model Selection, Adaptive Window Selection