Threshold Expectile Regressions With an Unknown Threshold for Dependent Data

Abstract

This article introduces a threshold expectile regression model with an unknown threshold for dependent data, which enables simple characterization of nonlinearity and heteroscedasticity in economic and financial applications. Profile estimation is proposed for the unknown parameters, and a sup-Wald test is developed to test the existence of the threshold effect at a fixed expectile level. Inference issues across multiple expectile levels are further considered, with a likelihood-ratio-type test designed to check for the presence of a common threshold value. Monte Carlo simulations demonstrate the nice finite sample performance of the proposed inference procedures. Finally, an empirical application demonstrates that the debt-to-GDP ratio has a heterogeneous threshold effect on the U.S. growth rate across the growth distribution.