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Multifractal dynamics of stock markets

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  • Dariusz Grech
  • Lukasz Czarnecki

Abstract

We present a comparative analysis of multifractal properties of financial time series built on stock indices from developing (WIG) and developed (S&P500) financial markets. It is shown how the multifractal image of the market is altered with the change of the length of time series and with the economic situation on the market. We emphasize that the proper adjustment of scaling range for multiscaling power laws is essential to obtain the multifractal image of time series. We analyze in this paper multifractal properties of real financial time series using H\"older $f(\alpha)$ representation and multifractal-DFA method. It is also investigated how multifractal properties of stocks change with variety of "surgeries" done on the initial real financial time series. This way we reveal main phenomena on the market influencing its multifractal dynamics. In particular, we focus on examining how multifractal picture of real time series changes when one cuts off extreme events like crashes or rupture points, and how fluctuations around the main trend in time series influence the multifractal behavior of financial series in the long-time horizon for both developed and developing markets.

Suggested Citation

  • Dariusz Grech & Lukasz Czarnecki, 2009. "Multifractal dynamics of stock markets," Papers 0912.3390, arXiv.org.
    • Handle: RePEc:arx:papers:0912.3390
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    Cited by:

    1. Suchetana Sadhukhan & Poulomi Sadhukhan, 2022. "Sector-wise analysis of Indian stock market: Long and short-term risk and stability analysis," Papers 2210.09619, arXiv.org.
    2. Chen, Feier & Miao, Yuqi & Tian, Kang & Ding, Xiaoxu & Li, Tingyi, 2017. "Multifractal cross-correlations between crude oil and tanker freight rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 474(C), pages 344-354.

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