ABSTRACT
This chapter examines common cycles, with both coincident and phase-shifting attributes, in the economy involving real estate. Common cycle analysis is, in a sense, an extension of common trend analysis which has been popular in more than a decade and proved useful in investigating the long-run relationship between economic variables. Common cycles differ from common trends in that the phase matters in the former; whereas there is no role for it in the latter. With common trends and cointegration analysis, one of the properties can be stated as: if xt is cointegrated with yt, then xt is also cointegrated with yt-1. However, this does not hold in common cycle analysis. It is possible that xt and yt have no common cycle but xt and yt-1 share a common cycle. This nature is important because usually economic fluctuations and movement are not in the same phase. Without phase-shifting operators, any common fluctuations and common cyclical movement, other than those coincident, would be left undetected, and a possible economic relation would be overlooked. Real estate is one of the variables which have noticeable cyclical characteristic but may not be in the same phase as the aggregate economic fluctuations. Therefore, analysis on phase-shifting common cycles, in addition to coincident common cycles, would have profound implications in real estate research. In addition, as the usual time domain methods for phase-shifting relations are empirically difficult to implement, frequency domain analysis is also employed in the chapter. In fact, spectral analysis is particularly useful and easy to understand regarding cycles and their phase.
