Testing Alpha in High Dimensional Linear Factor Pricing Models with Dependent Observations

TL;DR

This paper proposes three novel testing methods for alpha in high-dimensional linear factor models with dependent data, addressing dense and sparse alternatives and validated through simulations and real data.

Contribution

Introduction of three testing procedures tailored for dependent observations in high-dimensional factor models, including sum-type, max-type, and Cauchy combination tests.

Findings

Sum-type test performs well for dense alternatives.

Max-type test is effective for sparse alternatives.

Proposed methods are validated via simulations and real data.

Abstract

In this study, we introduce three distinct testing methods for testing alpha in high dimensional linear factor pricing model that deals with dependent data. The first method is a sum-type test procedure, which exhibits high performance when dealing with dense alternatives. The second method is a max-type test procedure, which is particularly effective for sparse alternatives. For a broader range of alternatives, we suggest a Cauchy combination test procedure. This is predicated on the asymptotic independence of the sum-type and max-type test statistics. Both simulation studies and practical data application demonstrate the effectiveness of our proposed methods when handling dependent observations.