Abstract. 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 of its cyclical behavior at different time scales. In this paper, the issues of cross-spectral analysis and filtering are concisely broached, dwelling in particular upon the windowed filter (Iacobucci and Noullez, 2005). In order to show the usefulness of these tools, an application to real data --- namely to US unemployment and inflation --- is presented. By means of cross spectral analysis and filtering, a correlation can be found between these two quantities (i.e. the Phillips curve) in some specific frequency bands, even if it does not appear in raw data.
Keywords: spectral and cross-spectral methods, frequency selective filters, US Phillips curve.