Journal
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
Volume 390, Issue 23-24, Pages 4304-4316Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.physa.2011.06.054
Keywords
Non-stationary time series; Wavelet transform; Fractals; Power law
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Funding
- Department of Science and Technology (DST-CMS) [SR/54/MS:516/07]
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We make use of wavelet transform to study the multi-scale, self-similar behavior and deviations thereof, in the stock prices of large companies, belonging to different economic sectors. The stock market returns exhibit multi-fractal characteristics, with some of the companies showing deviations at small and large scales. The fact that, the wavelets belonging to the Daubechies' (Db) basis enables one to isolate local polynomial trends of different degrees, plays the key role in isolating fluctuations at different scales. One of the primary motivations of this work is to study the emergence of the k(-3) behavior [X. Gabaix, P. Gopikrishnan, V. Plerou, H. Stanley, A theory of power law distributions in financial market fluctuations, Nature 423 (2003) 267-270] of the fluctuations starting with high frequency fluctuations. We make use of Db4 and Db6 basis sets to respectively isolate local linear and quadratic trends at different scales in order to study the statistical characteristics of these financial time series. The fluctuations reveal fat tail non-Gaussian behavior, unstable periodic modulations, at finer scales, from which the characteristic k(-3) power law behavior emerges at sufficiently large scales. We further identify stable periodic behavior through the continuous Morlet wavelet. (C) 2011 Elsevier B.V. All rights reserved.
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