Random walk and breaking trend in financial series: An econometric critique of unit root tests

The present note sheds light on several pitfalls associated with unit root tests that are overlooked by a growing volume of literature in financial economics. Specifically, several studies have confused unit root tests with the Random Walk hypothesis. Unit root tests are not designed for such a task since they aim at investigating whether a time series is difference-stationary or trend-stationary and are not, therefore, predictability tests. Secondly, we emphasize some serious shortcomings associated with the widely used unit root test developed by Zivot and Andrews [Zivot, E. & Andrews, D.W.K. (1992). Further evidence on the great crash, the oil-price shock, and the unit-root hypothesis. Journal of Business and Economic Statistics, 10, 251-270.]. In particular, we stress that results from the Zivot-Andrews test are sensitive to the methods employed to calculate the critical values and to select the maxim lag k. Furthermore, Zivot-Andrews test imposes a one time structural break in a time series; however recent studies showed that not counting for other true structural breaks may bias the results and may cause a spurious rejection of the unit root null hypothesis. Finally, we support our arguments by an empirical example based on the findings of Narayan and Smyth [Narayan, K.P. & Smyth, R. (2004). Is South Korea's stock market efficient? Applied Economics Letters, 11, 707-710.] with regards to the efficiency of South Korean stock market. We show that contrary to what the authors claim, the KSE (KOSPI) price index is predictable, and hence the South Korean stock market is not informationally efficient.