A three-pole filter understanding of the average value of a Fourier series and comparison with Hodrick-Prescott filter

Minskya, Ksovim (2016): A three-pole filter understanding of the average value of a Fourier series and comparison with Hodrick-Prescott filter.

Abstract

This paper develops a method of analyzing average value of a complex-valued function that can be represented as a Fourier series satisfying a few realistic restrictions. This method may be useful when Discrete Fourier transform is highly inefficient, and comparison with Hodrick-Prescott filter is made.

• Item Type: MPRA Paper
• Language: English
• Keywords: filtering, time series, hodrick-prescott, z-transform, average value, linear trend
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C19 - Other; C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C49 - Other; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C59 - Other; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C69 - Other; E - Macroeconomics and Monetary Economics > E3 - Prices, Business Fluctuations, and Cycles > E32 - Business Fluctuations ; Cycles

References

Bahar E. (1972). ''The indefinite Z-transform technique and application to analysis of difference equations'', Journal of Engineering Mathematics 6 (2): 125--132

Bhat N. et al. (2004). ``Computing Nash Equilibria of action-graph games'', Proceedings of the Twentieth Conference on Uncertainty in Artificial Intelligence 2004.

King, R.G. et al. (1993). ``Low frequency filtering and real business-cycle'', Journal of Economic Dynamics and Control 17: 207--231

Mavronicolas, M. et al. (2005). ``A graph-theoretic network security game'', WINE 2005: 969--978

Tsai, S. C., et al. (1983). ``Application of the z-transform method to the solution of the wave equation'', Journal of Sound and Vibration 19 (1): 17-20.