Response Surface Models for OLS and GLS Detrending-based Unit-root Tests in Nonlinear ESTAR Models

Abstract

In this article, we calculate response surface models for a large range of quantiles of the Kapetanios, Shin, and Snell (2003, Journal of Econometrics 112: 359–379) and Kapetanios and Shin (2008, Economics Letters 100: 377–380) tests for the null hypothesis of a unit root against the alternative—that the series of interest follows a globally stationary exponential smooth transition autoregressive process. The response surface models allow estimation of finite-sample critical values and approximate p-values for different combinations of the number of observations, T, and the lag order in the test regression, p. The latter can be either specified by the user or optimally selected using a data-dependent procedure. We present the new commands kssur and ksur and illustrate their use with an empirical example.