View article

A number of economic, financial, and climatic time series exhibit persistent cycles which are characterised by dependence patterns and peaks in the spectrum. In this paper, we introduce a class of cyclically-integrated models which enables the modelling of random cyclical patterns in stationary and non-stationary time series. We develop a theoretical background and asymptotic estimation theory for the cyclicality parameter representing the location of the peak in the spectrum. It is easy to implement and allows for the construction of narrow confidence intervals around the location point. Monte Carlo simulations confirm the good finite sample performance of our estimator. We illustrate our estimation procedure with three empirical applications. We uncover (quasi-) periodic cycles in macroeconomic series, both nominal and real (US nominal GDP and real industrial production), and CO2 concentration levels.