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Stochastic processes with power-law stability and a crossover in power-law correlations

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  • Podobnik, Boris
  • Grosse, Ivo
  • Eugene Stanley, H

Abstract

Motivated by the goal of finding a more accurate description of the empirically observed dynamics of financial fluctuations, we propose a stochastic process that yields three statistical properties: (i) short-range autocorrelations in the index changes, (ii) long-range correlations in the absolute values of the index changes, with a crossover between two power-law regimes at approximately one week, and (iii) power-law stability in the tails of the probability distributions of the index changes. We find that this stochastic process can surprisingly well reproduce statistical properties observed in the high-frequency data of the S&P 500 stock index.

Suggested Citation

  • Podobnik, Boris & Grosse, Ivo & Eugene Stanley, H, 2002. "Stochastic processes with power-law stability and a crossover in power-law correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 153-159.
    • Handle: RePEc:eee:phsmap:v:316:y:2002:i:1:p:153-159
    DOI: 10.1016/S0378-4371(02)01023-3
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    Cited by:

    1. Faheem Aslam & Paulo Ferreira & Haider Ali & Ana Ercília José, 2022. "Application of Multifractal Analysis in Estimating the Reaction of Energy Markets to Geopolitical Acts and Threats," Sustainability, MDPI, vol. 14(10), pages 1-23, May.
    2. Aslam, Faheem & Aziz, Saqib & Nguyen, Duc Khuong & Mughal, Khurrum S. & Khan, Maaz, 2020. "On the efficiency of foreign exchange markets in times of the COVID-19 pandemic," Technological Forecasting and Social Change, Elsevier, vol. 161(C).
    3. Arshad, Shaista & Rizvi, Syed Aun R. & Ghani, Gairuzazmi Mat & Duasa, Jarita, 2016. "Investigating stock market efficiency: A look at OIC member countries," Research in International Business and Finance, Elsevier, vol. 36(C), pages 402-413.
    4. Wang, Yiduan & Zheng, Shenzhou & Zhang, Wei & Wang, Jun & Wang, Guochao, 2018. "Modeling and complexity of stochastic interacting Lévy type financial price dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 499(C), pages 498-511.
    5. Azzam, Islam & El-Masry, Ahmed A. & Yamani, Ehab, 2023. "Foreign exchange market efficiency during COVID-19 pandemic," International Review of Economics & Finance, Elsevier, vol. 86(C), pages 717-730.
    6. Tao, Chen & Zhong, Guang-Yan & Li, Jiang-Cheng, 2023. "Dynamic correlation and risk resonance among industries of Chinese stock market: New evidence from time–frequency domain and complex network perspectives," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 614(C).

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