A Monte Carlo Investigation of Unit Root Tests and Long Memory in Detecting Mean Reversion in I(0) Regime Switching,Structural Break,and Nonlinear Data

The potential observational equivalence between various types of nonlinearity and long memory has been recognized by the econometrics community since at least the contribution of Diebold and Inoue (2001 Diebold, F., Inoue, A. (2001). Long memory and regime switching. Journal of Econometrics 105:131–159.[Crossref], [Web of Science ®] , [Google Scholar]). A large literature has developed in an attempt to ascertain whether or not the long memory finding in many economic series is spurious. Yet to date, no study has analyzed the consequences of using long memory methods to test for unit roots when the “truth” derives from regime switching, structural breaks, or other types of mean reverting nonlinearity. In this article, I conduct a comprehensive Monte Carlo analysis to investigate the consequences of using tests designed to have power against fractional integration when the actual data generating process is unknown. I additionally consider the use of tests designed to have power against breaks and threshold nonlinearity. The findings are compelling and demonstrate that the use of long memory as an approximation to nonlinearity yields tests with relatively high power. In contrast, misspecification has severe consequences for tests designed to have power against threshold nonlinearity, and especially for tests designed to have power against breaks.