Testing Alpha in High-Dimensional Conditional Time-Varying Factor Models with Dependent Observations

2026-04-15

AI Summary

This study addresses the inference problem for alpha significance in asset pricing models under high-dimensional settings with time-varying factor loadings and temporally dependent observations. The authors establish, for the first time, a stochastic expansion for the alpha estimator and demonstrate the asymptotic independence between sum- and max-type test statistics. They propose an adaptive Cauchy combination test that integrates B-spline sieve methods to model time-varying structures, while employing a block bootstrap for calibration and extreme value theory—specifically Gumbel convergence—to handle high-dimensional dependence. The method is valid under both dense and sparse alternative hypotheses. Simulation studies confirm its accurate size control and strong power across various alternatives, and empirical analysis demonstrates its effectiveness and practical utility in testing asset pricing models.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Cognitive Modeling & Cognitive Systems: Adaptive Behavior
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Models for Web evolution

Abstract

This paper studies alpha testing in a high-dimensional conditional time-varying factor model with temporally dependent observations. Both factor loadings and alpha processes are allowed to vary smoothly over time, and the cross-sectional dimension may be comparable to or larger than the sample size. Using a B-spline sieve method, we develop a sum-type test for dense alternatives, a max-type test for sparse alternatives, and a Cauchy combination test for adaptive inference. On the theoretical side, we derive explicit stochastic expansions for the estimated average alphas, establish asymptotic normality of the sum statistic, and develop the extreme-value limit theory for the max statistic by showing its Gumbel convergence under temporal dependence together with the validity of block-bootstrap calibration. We further prove asymptotic independence between the sum and max statistics and thereby justify the Cauchy combination test. Simulation results demonstrate that the proposed procedures achieve satisfactory size control and competitive power across a wide range of dense and sparse alternatives. An empirical application further illustrates the usefulness of the proposed methods in testing asset-pricing models with time-varying structure.

Problem

• alpha testing
• high-dimensional
• time-varying factor model
• temporal dependence
• asset pricing

Innovation

• time-varying factor model
• high-dimensional inference
• B-spline sieve
• Cauchy combination test
• extreme-value theory