Finite-Sample Sign-Based Inference in Linear and Nonlinear Regression Models with Applications in Finance

Abstract

We review several exact sign-based tests that have been recently proposed for testing orthogonality between random variables in the context of linear and nonlinear regression models. The sign tests are very useful when the data at the hands contain few observations, are robust against heteroskedasticity of unknown form, and can be used in the presence of non-Gaussian errors. These tests are also flexible since they do not require the existence of moments for the dependent variable and there is no need to specify the nature of the feedback between the dependent variable and the current and future values of the independent variable. Finally, we discuss several applications where the sign-based tests can be used to test for multi-horizon predictability of stock returns and for the market efficiency.

Pair copula constructions of point-optimal sign-based tests for predictive linear and nonlinear regressions

“…Hence, under mild assumptions these procedures are distribution-free and do not suffer from the issues encountered by t-type statistics in finite samples. These class of tests are valid in the presence of non-normal distributions and heteroskedasiticty of unknown form [see Boldin et al (1997) and Taamouti (2015) for a review of sign-based tests]. Furthermore, Dufour and Taamouti (2010) show that the heteroskedasticity and autocorrelation corrected tests developed by White (1980) (more commonly referred to as "HAC" procedures) are plagued with low power when the errors follow GARCH-type structures or there is a break in variance.…”