Periodic Unobserved Component Time Series Models: estimation and forecasting with applications

Periodic time series analysis refers to the modelling approach where important time series properties depend on the period of the year. The standard approach to time series modelling is to treat a time series as a stochastic process with seasonal fluctuations. In a periodic analysis seasonal variations are modelled using separate yearly time series for each season, which do not possess seasonal dynamics by construction. If the seasonal subseries are unrelated, periodic analysis simply implies a repeated analysis for each season. If the seasonal subseries are related, periodic analysis requires a truly multivariate time series approach for the seasonal subseries. This paper explores the periodic analysis in the context of unobserved components time series models which decompose a time series into components of interest including trend, seasonal and irregular. We compare five approaches. Standard nonperiodic structural time series modelling, periodic univariate unobserved components modelling of seasonal subseries, homogeneous multivariate unobserved components modelling, common trend modelling and seemingly unrelated unobserved components time series modelling. We confine ourselves to cases where estimation, diagnostic checking and forecasting, can be carried out easily and interactively using existing user-friendly software packages. We illustrate the methodology using three quarterly time series of energy demand (electricity, gas and coal) in the UK. We demonstrate that a periodic analysis is relatively straightforward and that it can be a viable alternative to the more parsimonious standard approach.