Improved modelling of evolving seasonal and cyclical time series
by
John Haywood
Victoria University of Wellington

Evolving seasonality (or cyclical behaviour) is often modelled with a state space representation, both to aid interpretability of the model and to take advantage of estimation via the Kalman filter. A new state space representation for seasonal or cyclical models is presented, that allows maximum generality of the spectral shapes which can be fitted well, from within a general class. It is shown that commonly used models do not share this flexibility and further that the use of the Kalman filter for estimation prevents such flexible models from being fitted. Examples of parsimonious models are also presented, to illustrate that while sometimes necessary, the new spectral flexibility need not result in overly complex model forms.

Date received: September 17, 2001