A Structural Time Series Model Facilitating Flexible Seasonality

We shed light on a class of models that increase the flexibility of the seasonal pattern within a framework of the structural time series model. The basic idea is to drive the seasonal summation model by a moving average process rather than by a white noise or an AR process. Generally, such an approach can be exhaustive in parameters, but the proposed model is parsimonious in the sense that we have only one extra parameter compared to the basic structural time series model. Because we stay at the linear Gaussian assumption, the estimation is quite easy and fast. The state space representation of the model is also given. An interpretation of moving average driven seasonal model is provided in terms of the offset effect on the pseudo-spectrum around the seasonal frequencies. The empirical analysis demonstrates that the proposed method is richly expressive in estimating the seasonal component, and is also supported by the minimum AIC procedure. A few cases where the proposed method is not working well provide us some useful information on the possible misspecification. Focusing attention on the two key quantities implied by the estimated models, we propose a graphical representation for the estimated models that help us to discover the unsuccessful cases and to confirm whether or not the alternative specification improves the modeling. Subject Area: Seasonal adjustment techniques: comparison of alternative methods