Spectral Analysis for Economic Time Series

The last ten years have witnessed an increasing interest of the econometrics community in spectral theory. In fact, decomposing the series evolution in periodic contributions allows a more insightful view of its structure and on its cyclical behavior at different time scales. In this paper I concisely broach the issues of cross-spectral analysis and filtering, dwelling in particular upon the windowed filter (Iacobucci and Noullez 2002). In order to show the usefulness of these tools, I present an application to real data, namely to US unemployment and inflation. I show how cross spectral analysis and filtering can be used to find correlation between them (i.e. the Phillips curve) in some specific frequency bands, even if it does not appear in raw data.