A critical investigation on detrending procedures for non-linear processes

The purpose of this paper is twofold. First, we study theoretically the impact of mis-specifying the trend upon the correlation structure of the process that has generated the observations. In particular, we consider the cases of (i) a regression on integrated processes and (ii) differencing processes with a deterministic trend. Second, we assess the effects of such mis-specifications on hypothesis testing when the data generating process is non-linear. The performances of several commonly employed tests for detecting the presence of a unit root and of non-linearity are investigated in a large scale simulation study. In particular, we will focus on some cases that can violate the assumptions at the basis of the application of the tests but, at the same time, represent situations commonly encountered in the field of Macroeconomics. The results suggest that much care has to be dedicated to the detrending procedure since a wrong specification can bias severely the subsequent analysis.