Properties of Higher Order Stochastic Cycles

This article investigates a general class of stochastic cycles, presenting the main properties in the time and frequency domains. Harvey and Trimbur [Review of Economics and statistics (2003) Vol. 85, pp. 244-55] showed how generalized cyclical processes may be used in unobserved components models to extract smoother cycles in economic series. The stochastic cycle models allow for a flexible description of periodic behaviour in time series data. In the frequency domain, a wide variety of peaked spectral shapes, characteristic of time-varying cyclical dynamics, is produced. The parameters have a direct interpretation, so cyclical behaviour may be studied directly; in a Bayesian approach, the researcher may implement prior views on the period in a consistent way. Extensions to multivariate models are possible