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Burst and inter-burst duration statistics as empirical test of long-range memory in the financial markets

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  • V. Gontis
  • A. Kononovicius

Abstract

We address the problem of long-range memory in the financial markets. There are two conceptually different ways to reproduce power-law decay of auto-correlation function: using fractional Brownian motion as well as non-linear stochastic differential equations. In this contribution we address this problem by analyzing empirical return and trading activity time series from the Forex. From the empirical time series we obtain probability density functions of burst and inter-burst duration. Our analysis reveals that the power-law exponents of the obtained probability density functions are close to $3/2$, which is a characteristic feature of the one-dimensional stochastic processes. This is in a good agreement with earlier proposed model of absolute return based on the non-linear stochastic differential equations derived from the agent-based herding model.

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  • V. Gontis & A. Kononovicius, 2017. "Burst and inter-burst duration statistics as empirical test of long-range memory in the financial markets," Papers 1701.01255, arXiv.org.
    • Handle: RePEc:arx:papers:1701.01255
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    References listed on IDEAS

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    Cited by:

    1. Rytis Kazakevicius & Aleksejus Kononovicius & Bronislovas Kaulakys & Vygintas Gontis, 2021. "Understanding the nature of the long-range memory phenomenon in socioeconomic systems," Papers 2108.02506, arXiv.org, revised Aug 2021.
    2. Vygintas Gontis & Aleksejus Kononovicius, 2019. "Bessel-like birth-death process," Papers 1904.13064, arXiv.org, revised Oct 2019.
    3. Vygintas Gontis, 2021. "Order flow in the financial markets from the perspective of the Fractional L\'evy stable motion," Papers 2105.02057, arXiv.org, revised Nov 2021.
    4. Vygintas Gontis & Aleksejus Kononovicius, 2017. "The consentaneous model of the financial markets exhibiting spurious nature of long-range memory," Papers 1712.05121, arXiv.org, revised Feb 2018.
    5. Gontis, V. & Kononovicius, A., 2020. "Bessel-like birth–death process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    6. Rytis Kazakeviv{c}ius & Aleksejus Kononovicius, 2023. "Anomalous diffusion and long-range memory in the scaled voter model," Papers 2301.08088, arXiv.org, revised Feb 2023.
    7. Gontis, V. & Kononovicius, A., 2018. "The consentaneous model of the financial markets exhibiting spurious nature of long-range memory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 1075-1083.
    8. Aleksejus Kononovicius & Vygintas Gontis, 2019. "Approximation of the first passage time distribution for the birth-death processes," Papers 1902.00924, arXiv.org.
    9. Vygintas Gontis & Aleksejus Kononovicius, 2017. "Spurious memory in non-equilibrium stochastic models of imitative behavior," Papers 1707.09801, arXiv.org.
    10. Wang, Guochao & Zheng, Shenzhou & Wang, Jun, 2020. "Fluctuation and volatility dynamics of stochastic interacting energy futures price model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).

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