A Study Towards a Dynamic Theory of Seasonality for Economic Time Series

Traditionally One Decomposes Economic Time Series Exhibiting Seasonality in a Cyclical Component, a Seasonal Component and Possibly Other Components. the Fundamental Assumptions Almost Exclusively Made About This Decomposition Is That (1) the Components Are Mutually Orthogonal and (2) the Seasonal Component Has Power Only At the Seasonal Frequency and Its Harmonics. in This Paper We Discuss the Fact That in the Context of Dynamic Economic Models Such a Decomposition Is Usually Inappropriate for the Endogenous Variables of the Model. We Discuss Three Possible Decompositions, Including the Traditional Decomposition, Analyze Their Properties and Digress on the Relevant Use of the Decompositions We Define. the Paper Also Discusses Ways to Estimate Dynamic Models with Seasonality, Yielding the Relevant Decomposition, Via the Mle Approach. It Is Shown That the Traditional Decomposition of an Endogenous Variable Typically Does Not Coincide with What We Believe Is a Relevant Decomposition of That Variable Along the Lines of the Exogenous Seasonal and Cyclical Sources of the Model.