Analysis of Economic Cycles Using Unobserved Components Models

The Unobserved Components Models represent a framework in which phenomena like any periodic behaviour, economic cycles in particular, may be modelled and forecast naturally. The main distinct feature of the methodology used in this paper is the use of a Dynamic Harmonic Regression model, characterised by time variable parameters that may vary following a rich family of models. This class of models are set up in a State Space context that takes advantage of the extraordinary flexibility of the recursive algorithms known as the Kalman Filter and Fixed Interval Smoother. Different versions of the models have to be applied to time series, depending on their time properties. In particular, time series with a non-constant period cycle has to be analysed in a totally different way to other series that exhibit a constant period cycle. A simple method to extract the cyclical information from the series in the case of non-constant period cycles is presented in the paper. The methodology is compared with others and shown working in practice with several examples.