Testing for Stationarity at High Frequency

The high frequency behavior of the KPSS test, which is most commonly used to test for stationarity, is analyzed in a continuous time framework. Our asymptotics show that the test has no discriminatory power at high frequency: It either always rejects stationarity or has no nontrivial power at high frequency. The test becomes valid at high frequency only when the bandwidth of its longrun variance estimate is chosen suitably in our framework. We also analyze the residual-based KPSS test for cointegration.