High‐dimensional non‐parametric tests for linear asset pricing models

Abstract

This paper develops a novel non‐parametric test for testing the high‐dimensional alpha in linear asset pricing models, where the number of securities can be much larger than the time‐dimension of the return series. The asymptotic null distribution and the local power property are established for a class of weighted spatial‐sign tests, which results in an optimal test INST by choosing the weight function as the inverse of the norm. The INST test is optimal in the sense that it is locally most powerful within this class. As a non‐parametric test, the INST test is also robust to the departures from normality of the error distribution. Monte Carlo simulation and empirical study with real financial data show the superiority of INST test in terms of both robustness and efficiency.

Spatial-sign based High Dimensional White Noises Test

“…Zou et al (2014), Feng and Liu (2017) also extend the spatial-sign based method to the high dimensional sphericity test. Some spatial-sign based test procedures for high dimensional alpha test in factor pricing model are proposed by Liu et al (2023), Zhao et al (2022), Zhao (2023). In an important work, Paindaveine and Verdebout (2016) proposed a spatial-sign based test for i.i.d-ness against serial dependence.…”

“…So γ t = O p (p −1/2 ). Thus, by taking the same procedure as the proof of Theorem 1 in Zhao et al (2022), we have…”