The Nonstationarity-Complexity Tradeoff in Return Prediction

TL;DR

This paper introduces a novel model selection method for stock return prediction in non-stationary environments, balancing model complexity and training window size to improve predictive accuracy and trading performance.

Contribution

It proposes a tournament-based adaptive model selection approach that jointly optimizes model class and training window size considering non-stationarity, backed by theoretical analysis and empirical validation.

Findings

Outperforms standard benchmarks with 14-23% higher out-of-sample R^2.

Achieves positive R^2 during major recessions, unlike benchmarks.

Yields 31% higher cumulative returns in trading strategies.

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 non-stationarity. 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 80bps 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.