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Characterizing Multi-Scale Self-Similar Behavior and Non-Statistical Properties of Financial Time Series


  • Sayantan Ghosh
  • P. Manimaran
  • Prasanta K. Panigrahi


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 \cite{hes5} 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.

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  • Sayantan Ghosh & P. Manimaran & Prasanta K. Panigrahi, 2010. "Characterizing Multi-Scale Self-Similar Behavior and Non-Statistical Properties of Financial Time Series," Papers 1003.2539,, revised Dec 2010.
  • Handle: RePEc:arx:papers:1003.2539

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    1. Olivier V. Pictet & Michel M. Dacorogna & Ulrich A. Muller, 1996. "Heavy tails in high-frequency financial data," Working Papers 1996-12-11, Olsen and Associates.
    2. Olivier V. Pictet & Michel M. Dacorogna & Ulrich A. Muller, 1996. "Hill, Bootstrap and Jackknife Estimators for Heavy Tails," Working Papers 1996-12-10, Olsen and Associates.
    3. Plerou, Vasiliki & Gopikrishnan, Parameswaran & Rosenow, Bernd & Amaral, Luis A.N. & Stanley, H.Eugene, 2000. "Econophysics: financial time series from a statistical physics point of view," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 279(1), pages 443-456.
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