Conformal Prediction For Financial Time Series Under Asset Pricing Models

Abstract

While numerous statistical approaches for uncertainty quantification have been proposed, most rely on parametric assumptions that are often violated in financial markets, and research on distribution-free variability estimation remains limited. We explore the application of conformal prediction methods to financial time series and provide a comprehensive comparison with classical econometric techniques for constructing stock return prediction intervals. The conformal prediction methods examined include Inductive Conformal Prediction, Ensemble Batch Prediction Intervals, Mondrian Conformal Prediction, and Time-Weighted Conformal Prediction. These distribution-free approaches are systematically compared against classical parametric methods, comprising Heteroskedasticity and Autocorrelation Consistent robust ordinary least squares and GARCH-based dynamic conditional heteroskedasticity intervals. The evaluation employs both the Capital Asset Pricing Model and the Fama-French three-factor model as empirical testing frameworks, using daily return data from four securities representing diverse market characteristics: NVIDIA Corporation, Alphabet Inc., JPMorgan Chase \& Co., and The Coca-Cola Company. Inductive Conformal Prediction (ICP) provides robust coverage but wider intervals, while adaptive methods trade reliability for efficiency. Classical volatility models remain competitive, and multi-factor frameworks improve moderate-volatility performance but weaken coverage for highly volatile assets.