# Spectral Analysis Applied to Financial Time Series

Spectral analysis can be used to identify and to quantify the different frequency components of a data series. Filters permit to capture speci fic components (e.g. trends, cycles, seasonalities) of the original time-series. Both spectral analysis and standard fi ltering methods have two main drawbacks: (i) they impose strong restrictions regarding the possible processes underlying the dynamics of the series (e.g. stationarity), and, (ii) they lead to a pure frequency-domain representation of the data, i.e. all information from the time-domain representation is lost in the operation. In this project, and in the first step, we discuss spectral analysis and fi ltering methods to gather information about the frequency components of a time-series.

In the second step, we introduce wavelets, which are relatively new tools in economics and finance. They take their roots from fi ltering methods and Fourier analysis. But they overcome most of the limitations of these two methods. Indeed their principal advantages are the following: (1) they combine information from both time-domain and frequency-domain and, (2) they are also very flexible and do not make strong assumptions concerning the data generating process for the series under investigation.