TAILIEUCHUNG - An illustration of harmonic regression based on the results of the fast fourier transformation

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. | Yugoslav Journal of Operations Research 12 (2002), Number 2, 185-201 AN ILLUSTRATION OF HARMONIC REGRESSION BASED ON THE RESULTS OF THE FAST FOURIER TRANSFORMATION* Imre BêRTFAI Technical Faculty, University of P›cs, Hungary bartfai@upisun, 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 timedomain 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. Keywords: Time series, forecasting, regression, Fourier-analysis. 1. INTRODUCTION The author must confess he has always been fascinated by the analytical capabilities of the Fourier-transformation and its multi-purpose character, rendering it well-usable in a variety of the scientific areas. However, the application of this method is often limited to the technical/engineering area, as the practical usage for a * An enhanced version of the paper presented at the occasion of EURO XVII, Budapest, 16-19th July, 2000. 186 I. B‹rtfai / An

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