In particular, I employ a structural time series (STS) or unobserved components methodology which allows for a direct empirical test of endogenous cycle theory against stochastic alternatives and/or mixed stochastic-endogenous models.
Thus the key issue in testing for an endogenous cycle is restricted to not whether [Rho] = 1 or [Rho] [not equal to] 1, but is rather the degree of damping.
A deterministic trend or a stochastic trend plus an endogenous cycle are evidence against the TS and DS hypotheses.
To make such an assessment operational, it is necessary to decompose the estimated cycle, [Mathematical Expression Omitted], in each time period into three components: 1) the pure endogenous cycle, EC; 2) the pure stochastic cycle, SC; and 3) the mixed endogenous-stochastic cycle, MC.
At that point, it becomes part of the endogenous cycle and loses its independent existence.
This result further establishes the relative importance of the endogenous cycle.
Given that most endogenous cycle theories are cast in terms of levels rather than growth rates, the DS plus cycle model fails to adequately incorporate endogenous cycles.
Among economists studying the business cycle, these tools are used to address questions such as whether cyclical movements in macroeconomic time series are the damped oscillations of a stable system reacting to exogenous, stochastic shocks, or are the result of endogenous cycles
in a nonlinear system.