An illustration of harmonic regression based on the results of the fast Fourier transformation

Abstract

The well-known methodology of the Fourier analysis is put against the background in the 2nd half of the century parallel to the development of the time-domain approach in the analysis of mainly economical time series. However, from the author's point of view, the former possesses some hidden analytical advantages which deserve to be re-introduced to the toolbox of analysts. This paper, through several case studies, reports research results for computer algorithm providing a harmonic model for time series. The starting point of the particular method is a harmonic analysis (Fourier-analysis or Lomb-periodogram). The results are optimized in a multifold manner resulting in a model which is easy to handle and able to forecast the underlying data. The results provided are particularly free from limitations characteristic for that methods. Furthermore, the calculated results are easy to interpret and use for further decisions. Nevertheless, the author intends to enhance the procedure in several ways. The method shown seems to be very effective and useful in modeling time series consisting of periodic terms. An additional advantage is the easy interpretation of the obtained parameters.