Non-invertibility and unobserved component estimation : with an application to seasonal adjustment

Abstract

The aim of this thesis is to shed some new light and cast in homogenous framework existing problems related to the extraction/removal of components from a time series. The term components is used for the moment in a very broad sense. Components are, for example, what is perceived to be the seasonal effect in the data, or the long run tendency, usually named trend, or the swinging patterns related to a cycle. In the first Section I will identify them in the frequency domain. It is not the aim of the work to define these components. This is the reason why I used the expression “what is perceived to be”, as the intuitive understanding of these concepts is immediate, but a universally accepted definition is an impossible task. I will rather focus on specific procedures, such as seasonal adjustment or removal of trend (detrending) from a series, and the properties that their application might transmit to the data. In particular, I will deal with the non-invertibility property that a series, freed from the influence of the component(s) in question, turns out to have at the end of the applied procedure, be that seasonal adjustment or detrending.