An illustration of harmonic regression based on the results of the fast Fourier transformation
DOI:
https://doi.org/10.2298/YJOR0202185BKeywords:
Time series, forecasting, regression, Fourier-analysis.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.References
Anderson, T.W. (1971) The statistical analysis of time series. New York, itd: Wiley
Bertfai, I. (1990) On prediction of time series using DFT. u: Procc. of XIV International Conference on Mathematical Programming, March, Metraheza, Hungary
Castiglioni, P. Lomb periodogram. http://www.cbi.polimit.it/glossary/Lomb.html
Fuller, W.A. (1995) Introduction to statistical time series. New York, itd: Wiley
Granger, C.W.J. (1966) The typical spectral shape of an economic variable. Econometrica, 34,(1), 150-161
Hesselmann, N. (1983) Digitale Signalverarbeitung. Wurzburg: Vogel
Hesselmann, N. (1985) Digitalilis Jelfeldolgozas. Budapest: Maszaki Konyvkiado
Hintze, J.L. (1991) Time series analysis and forecasting. BMDP Statistical Software Inc
Newton, H.J. Timeslab. http://stat.tamu.edu/jnewton
Osvald, K., Nagy, G., Vimi, J. (1981) Hangfrekvencis K'zponti Verz,rl,s. Budapest: Maszaki Konyvkiado
Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P. (1992) Numerical recipes in Fortran: The art of scientific computing. Cambridge, itd: Cambridge University Press / CUP
Qi, Y. (1997) A simulation laboratory to evaluation of dynamic traffic management system. Massachusetts: Center of Transportation Studies in Institute of Technology, doktorska disertacija
Sachs, L. (1974) Angewandte Statistik. Berlin, itd: Springer Verlag
Schlittgen, R., Streitberg, B.H.J. (1995) Zeitreihenanalyse. Munchen-Wien: Oldenbourg Verlag
Smith, L. (1998) NCEPH Seminar, Chapter Lorenz Curve and Gini Coefficient. http://www.ann.edu.au/nceph/inequalities/nceph-presentation, February
Stocker, H. (1995) Taschenbuch mathematischer Formeln und moderner Verfahren. Verlag Harri Deutsch
Varga-Haszonits, Z., Mahr, J. (1978) Az idojárás elorejelzése és a mindennapi élet. Budapest: Gondolat
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