Robust Spatial-Sign-Based Testing of High-Dimensional Alpha in Conditional Factor Models

TL;DR

This paper introduces a robust, adaptive spatial-sign-based testing framework for high-dimensional alpha in factor models, combining max-type and sum-type tests for improved power and resilience.

Contribution

It develops a new spatial-sign-based max-type test, derives its null distribution, and constructs an adaptive procedure combining it with a sum-type test for high-dimensional alpha testing.

Findings

The proposed test is robust to heavy-tailed distributions.

It maintains superior power across different sparsity levels.

Simulation and empirical results validate its effectiveness.

Abstract

This paper develops a new framework for alpha testing in high-dimensional factor pricing models with time-varying coefficients. To detect sparse alternatives, we propose a spatial-sign-based max-type test and derive its limiting null distribution. A key theoretical result is that our statistic is asymptotically independent of the spatial-sign-based sum-type test proposed by Zhao (2023). Exploiting this independence, we construct an adaptive testing procedure via the Cauchy combination method. This approach integrates the complementary strengths of both max-type and sum-type statistics, ensuring robust power across diverse sparsity levels. Extensive simulations and an empirical application demonstrate that the proposed test is resilient to heavy-tailed distributions and maintains superior performance under various alternative specifications.