Observable trend-projecting state-space models

Much attention has focused in recent years on the use of state-space models for describing and forecasting industrial time series. However, several state-space models that are proposed for such data series are not observable and do not have a unique representation, particularly in situations where the data history suggests marked seasonal trends. This raises major practical difficulties since it becomes necessary to impose one or more constraints and this implies a complicated error structure on the model. The purpose of this paper is to demonstrate that state-space models are useful for describing time series data for forecasting purposes and that there are trend-projecting state-space components that can be combined to provide observable state-space representations for specified data series. This result is particularly useful for seasonal or pseudo-seasonal time series. A well-known data series is examined in some detail and several observable state-space models are suggested and compared favourably with the constrained observable model.