Spectral and Wavelet Analysis

Spectral and wavelet analysis go beyond standard time domain approaches in econometrics and are able to address questions which cannot be answered by the latter. This work presents the periodogram as an intuitive measure to detect dominant cycles in data. Properties of the periodogram are given with proofs. Measures of interdependence of series in the frequency domain are discussed. The most prominent filter in business cycle theory, the Hodrick-Prescott filter, is compared with other linear filter by their gain and phase functions and their ability to remove unit roots. Eventually, it is shown that wavelet analysis is able to overcome the strict assumptions on a series when applying spectral analysis and captures important filter theory elements such as band-pass filtering. Presenting mathematical foundations to a reasonable extent as well as academic and real-world examples at length, this work aims at a widespread understanding and application of these tools in economic research.