Seasonal Specific Structural Time Series

The paper introduces the class of seasonal specific structural time series models, according to which each season follows specific dynamics, but is also tied to the others by a common random effect. Seasonal specific models are dynamic variance components models that account for some kind of periodic behaviour, such as periodic heteroscedasticity, and are also tailored to deal with situations such that one or a group of seasons behave differently. Trends and non periodic features can still be extracted and their nature is discussed. Multivariate extensions entertain the case when cointegration pertains only to groups of seasons. It is finally shown that a circular correlation pattern for the idiosyncratic disturbances yields a periodic component that is isomorphic to a trigonometric seasonal com- ponent.