Title: The $T$ ratio test for a bilinear unit root under general conditions with applications
Authors: Julio Angel Afonso-Rodriguez - University of the Balearic Islands (Spain) [presenting]
Abstract: Nonstationarity is a great stylized fact of many macroeconomic and financial time series, where the particular type of nonstationary behaviour determines its theoretical properties and conditions the inferential procedures to be used in their empirical analysis. We study a general class of globally nonstationary processes, called a stochastic unit root (STUR), which generalizes the fixed unit root case generating periods of stationary, nonstationary and explosive behaviour, and that contains several different particular cases as, e.g., the so-called bilinear unit root process (BLUR). For this process we propose a general weak limiting distribution in the case of possibly serially correlated error terms, and study the properties of some unit root tests under this representation, both against a stationary and a STUR alternative. Among these test statistics, we found that the $T$-ratio test for a BLUR alternative based on an augmented auxiliary regression automatically corrects for serially correlated regular error terms and for any choice of the number of lags (thus controlling the empirical size), and only shows a slight power loss for high values of the number of lags. We illustrate all these theoretical findings with an extensive simulation exercise and with several empirical applications.