The Nonstationarity-Complexity Tradeoff in Return Prediction

2025-12-29

AI Summary

This paper addresses the fundamental trade-off between model complexity and rolling window length in stock return forecasting under nonstationarity—where complex models reduce misspecification error but exacerbate nonstationarity-induced instability. We propose a tournament-based model selection framework that jointly optimizes model class and rolling window length using nonstationary validation data. Theoretically, our approach achieves balanced control over three sources of error: misspecification, estimation variance, and nonstationarity. Empirically, evaluated on 17 industry portfolios, it improves out-of-sample R² by 14–23% on average. Performance is especially pronounced during severe recessions—including the Gulf War and the 2008 financial crisis—where our strategy delivers 31% higher cumulative returns than the benchmark and, for the first time in extreme market turmoil, achieves positive out-of-sample R² (while the benchmark yields negative R²).

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Ensemble Methods
• Search and Optimization: Non-convex Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Resolves tradeoff between model complexity and non-stationarity in stock prediction.
• Proposes adaptive model selection optimizing training window and class jointly.
• Improves out-of-sample accuracy and economic returns in volatile market periods.

Innovation

• Jointly optimizes model class and training window size
• Uses tournament procedure on non-stationary validation data
• Balances misspecification error, estimation variance, and non-stationarity