MULTIFRACTAL BEHAVIOUR IN NATURAL GAS PRICES BY USING MF-DFA AND WTMM METHODS

We make a comparative study of Multifractal Detrended Fluctuation Analysis (MF-DFA) and the Wavelet Transform Modulus Maxima (WTMM) method to detect multifractal character of natural gas daily returns. We give a brief introduction on above methods and compare their effectiveness. The results from this methodoligies show that behaviour of natural gas daily returns were multifractal. The major sources of multifractality are long-range correlations of small and large fluctuations and Fat-tail distributions of the series

Keywords:

Natural Gas, Multifractal MF-DFA, WTMM,

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B.B. Manderlbrot,The Fractal Geometry ofNature, FreemanWH,New York, 1982.
W.Kantelhardt, S.A.Zschiegner, E.Koscienlny-Bunde, S. Havlin,Multifractal detrended fluctuation analysis of nonstationary time series,Physica A316 (2002) _114.
Muzy, J. F., Bacry, E. & Arneodo, A. (1994) The multifractal formalism revisited with wavelets. Int. J. Bifurc. Chaos. 4, 245-302. (1994)
Struzik. Z. R. (2000) Determining local singularity strengths and their spectra with the wavelet transform. Fractals 8, 163-179
Andrejs Puckovs, Andrejs Matvejevs, Wavelet Transform Modulus Maxima Approach for World Stock Index Multifractal Analysis.University,Information Technology and Management Science. pp76-86. Espen Ihlen (2012),”Introduction to multifractal detrended fluctuation analysis in
Matlab”,Frontiers in Physiology K. Matia, Y. Ashkenazy, H.E. Stanley, Multifractal properties of price fluctuations of stock and commodities, Europhysics Letter 61 (2003) 422–428.
Mallat, S. G. and Hwang, W. L. (1990). Technical Report #549, Computer
Science Department, New York University, unpublished. Muzy, J. F., Bacry, E. and Arneodo, A. (1991). Wavelets and multifractal formalism for singular signals: Application to turbulence data. Physical Review Letters, 67(25), 3515–3518.
Yalamova, R. (2003). Wavelet MRA of index patterns around financial market shocks. Ph.D. thesis, Kent State University.