The nonstationary feature of economic growth imposes a great challenge to theoretical economics and economic physics: how to identify some stable patterns from an evolving economy. Can we simplify the observed complex movements into some simple patterns by means of mathematical mapping? This is the Copernicus problem in macro econometrics. The time scale plays a critical role in observing business cycles. Measurement and theory cannot be separated from each other. The dynamic patterns from competing observation references can be seen in Figure 3.1. In econometrics, the linear filter of first differencing (FD) is widely applied to construct an equilibrium (short-term) picture of economic fluctuations. The resulting time series are erratic and short-correlated (Figure 3.1b). The random

walk model with a constant drift is also called the unit-root model in macro econometrics (Nelson and Plosser 1982). In neo-classical growth theory, the long-term equilibrium path is characterized by an exponential growth or a loglinear (LL) trend (Solow 1956). The resulting cycles are long-correlated. The problem is that measurement is sensitive to the choice of time boundaries.