MULTIFRACTAL ANALYSIS OF THE DYNAMICS OF TURKISH EXCHANGE RATE

Abstract

We perform a comparative study of applicability of the Multifractal Detrended Fluctuation Analysis (MFDFA) and the Wavelet Transform Modulus Maxima (WTMM) method in properly detecting of mono- and multifractal character of data. After summarizing the theory behind both methods, we apply both methods on USD/TRY currency. The results show that our data has multifractal nature but not at high level and multifractality is poorer if WTMM method is used. We also investigated whether other Eastern European country currencies, such as Russian Rubble and Hungarian Forint have multifractal characters by using MFDFA method. Therefore, forecasters have often encountered in trying to predict these exchange rates with models that do not incorporate any notion of inhomogeneity will have little predictive power.

Keywords

• MF-DFA,WTMM, USD/TRY, Eastern European currencies,

Kaynakça

1. B.B. Manderlbrot,The Fractal Geometry ofNature, FreemanWH,New York, 1982.
2. W. Kantelhardt, S.A. Zschiegner, E. Koscienlny-Bunde, S. Havlin, Multifractal detrended fluctuation analysis of nonstationary time series, Physica A316 (2002) _114.
3. Muzy, J. F., Bacry, E. & Arneodo, A. (1994) The multifractal formalism revisited with wavelets. Int. J. Bifurc. Chaos. 4, 245-302. (1994)
4. Struzik. Z. R. (2000) Determining local singularity strengths and their spectra with the wavelet transform. Fractals 8, 163-179
5. 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
6. 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.
7. Mallat, S. G. and Hwang, W. L. (1990). Technical Report #549, Computer
8. Science Department, New York University, unpublished.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.

9. Yalamova, R. (2003). Wavelet MRA of index patterns around financial market shocks. Ph.D. thesis, Kent State University.