Unit Root Test with High-Frequency Data

Deviations of asset prices from the random walk dynamic imply the predictability of asset returns and thus have important implications for portfolio construction and risk management. This paper proposes a real-time monitoring device for such deviations using intraday high-frequency data. The proposed procedure is based on unit root tests with in-fill asymptotics but extended to take the empirical features of high-frequency financial data (particularly jumps) into consideration. We derive the limiting distribution of the test statistic under both the null hypothesis of a random walk with jumps and the alternative of mean reversion/explosiveness with jumps. The limiting results show that ignoring the presence of jumps could potentially lead to severe size distortions of both the left-sided (against mean reversion) and right-sided (against explosive) unit root tests. The simulation results reveal the satisfactory performance of the test even with data from a relatively short time span (i.e., one quarter). As an illustration, we apply the procedure to the Nasdaq composite index at the 10-minute frequency from January 2, 1996 to December 8, 2017. We find strong evidence of explosiveness dynamics in asset prices during the dot-com bubble and the subprime mortgage crisis periods and mean reversion in the late 2015 and early 2016