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Approximation of data using non-integer harmonics series

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Abstract

This paper introduces a method for approximating real world data by means of non-integer harmonics series (NIHS). The NIHS terms are sinusoidal functions of arbitrary amplitude, frequency and phase shift that can be computed by direct numerical algorithms. Applications go from obtaining time derivatives up to forecasting future values. Three illustrative examples with the Dow Jones Industrial stock market index, the Europe Brent Spot Price FOB and the daily temperature records of New York city are studied. The results show the effectiveness of the NIHS when dealing with real world time data series.

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Acknowledgements

The authors acknowledge the Yahoo Finance (https://finance.yahoo.com/), the U.S. Energy Information Administration (http://www.eia.gov/dnav/pet/hist/LeafHandler. ashx?n=PET&s=RBRTE&f=D), and the University of Dayton - Environmental Protection Agency, Average Daily Temperature Archive (http://academic.udayton.edu/kissock/http/Weather/default.htm) for the data used in this paper.

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  1. Department of Electrical Engineering, Institute of Engineering, Polytechnic of Porto, R. Dr. António Bernardino de Almeida, 431, 4249-015, Porto, Portugal

    J. A. Tenreiro Machado

  2. UISPA–LAETA/INEGI, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465, Porto, Portugal

    António M. Lopes

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Correspondence to António M. Lopes.

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Tenreiro Machado, J.A., Lopes, A.M. Approximation of data using non-integer harmonics series. Nonlinear Dyn 89, 2845–2854 (2017). https://doi.org/10.1007/s11071-017-3629-4

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