A Simultaneous Test of Unit Root and Level Change

Testing the existence of unit root and/or level change is necessary in order to understand the underlying processes of time series. In many studies carried out so far, the focus was only on a single aspect of unit root and level change, therefore limiting a full assess to the given problems. Our study aims to find a solution to the given problems by testing the two hypotheses simultaneously.We derive the likelihood ratio test statistic based on the state space model, and their distributions are created by simulation method. The performance of the proposed method is validated by simulated time series and also applied to two Korean macroeconomic time series to confirm its practical application. This analysis can provide a solution to determine the underlying structure of arguable time series