Model specification, observational equivalence and performance of unit root tests

In this paper we highlight the necessity of new criteria for evaluation of performance of unit root tests. We suggest focusing directly on the reasons that create ambiguity in unit root test’s results. Two reasons for unsatisfactory properties of unit root tests can be found in the literature (i) the model misspecification and (ii) observational equivalence. Regarding first reason, there is immense literature on several components of model specification covering specification techniques, consequence of misspecification and robust methods. However complete model specification involves multiple decisions and most of studies on performance of unit root tests do not address issue of multiple specification decisions simultaneously. The Monte Carlo studies are conditional on some of implicit specification and for Monte Carlo; these specifications are by construction valid. But for real data, the implicit decisions are often not true and specification decisions need to be endogenized. A closer match with real case is possible if multiple specification decisions are endogenized, thus providing more reliable measure of performance of unit root tests. Second problem in differentiating trend and difference stationary process is the observational equivalence between two processes. We suggest exploring data generating processes with different long run dynamics and small sample equivalence so that a researcher should have an idea about other plausible models for a data set for which he has estimated some model.