Analysis of financial time series using wavelet methods

This chapter presents a set of tools, which allow gathering information about the frequency components of a time series. In a first step, we discuss spectral analysis and filtering methods. Spectral analysis can be used to identify and to quantify the different frequency components of a data series. Filters permit to capture specific components (e.g., trends, cycles, seasonalities) of the original time series. Both spectral analysis and standard filtering 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 a second step, we introduce wavelets, which are relatively new tools in economics and finance. They take their roots from filtering methods and Fourier analysis, but overcome most of the limitations of these two methods. Their principal advantages derive from (i) combined information from both time domain and frequency domain and (ii) their flexibility as they do not make strong assumptions concerning the data- generating process for the series under investigation