Auxiliary Regressions for Identification of Trend Stationarity

Abstract

This paper examines the performance of a mean reversion test based on the integration of trend stationarity (TS) and constrained autoregressive (CAR) tests. We study and document the behavior of the unified test under a random walk process, a TS process, a CAR process attributed to Jegadeesh, and a “Fads” process. We find evidence that the unified test can distinguish between unit root and trend stationary processes. Particularly, under a TS process the p-values of the models participating in the unified test gradually improve with aggregation and the best p-value is displayed by the TS test. We also find that under a TS process the magnitude of the slope coefficient tends to increase (in absolute value) with aggregation with the largest slope coefficient displayed by the TS process. In contrast, the patterns created by the unit root processes that we examine are markedly different.