Bubbles are characterized by rapid expansion followed by a contraction. Evans (1991) shows that stationarity tests suggested by Hamilton and Whiteman (1985) and Diba and Grossman (1988) are incapable of detecting periodically collapsing bubbles. Phillips, Wu, and Yu (2006) advanced the forward recursive unit root test which improves the power significantly in the presence of periodically collapsing bubbles. In this paper, we consider rolling window unit root test with a pre-selected optimum window. A combining use of conventional unit root test and forward recursive unit root test is suggested from the results of power comparison. Furthermore, we apply those three methods to test the existence of bubbles in Seoul apartment market and to locate the bubble period if they were present
