Long-range memory test by the burst and inter-burst duration distribution

  title={Long-range memory test by the burst and inter-burst duration distribution},
  author={Vygintas Gontis},
  journal={Journal of Statistical Mechanics: Theory and Experiment},
  • V. Gontis
  • Published 31 May 2020
  • Engineering
  • Journal of Statistical Mechanics: Theory and Experiment
It is empirically established that order flow in the financial markets is positively auto-correlated and can serve as an example of a social system with long-range memory. Nevertheless, widely used long-range memory estimators give varying values of the Hurst exponent. We propose the burst and inter-burst duration statistical analysis as one more test of long-range memory and implement it with the limit order book data comparing it with other widely used estimators. This method gives a more… 

Order flow in the financial markets from the perspective of the Fractional Lévy stable motion

  • V. Gontis
  • Mathematics
    Commun. Nonlinear Sci. Numer. Simul.
  • 2022

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The group has shown that the long-range memory phenomenon can be reproduced using various Markov processes well enough to match other statistical properties of the financial markets, such as return and trading activity distributions and first-passage time distributions.



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A stochastic differential equation is presented as a dynamical model of the observed memory in the financial time series and reproduces the statistical properties of the trading activity and serves as a background model for the waiting time, return and volatility.

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For the London Stock Exchange we demonstrate that the signs of orders obey a long-memory process. The autocorrelation function decays roughly as a power law with an exponent of 0.6, corresponding to

Spurious Memory in Non-Equilibrium Stochastic Models of Imitative Behavior

It is confirmed that the characteristic feature of the processes described by a one-dimensional SDE is the power-law exponent of the burst or inter-burst duration PDF, which might be used to detect spurious memory in various non-equilibrium systems, where observed macroscopic behavior can be derived from the imitative interactions of agents.


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A long memory property of stock market returns and a new model

A "long memory" property of stock market returns is investigated in this paper. It is found that not only there is substantially more correlation between absolute returns than returns themselves, but

Modeling long-range memory with stationary Markovian processes.

  • S. Miccichè
  • Mathematics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2009
This paper analytically investigates what is the relationship between the asymptotic decay of the autocorrelation function and the tails of the stationary pdf and provides simple stationary processes associated to Langevin equations with white noise thus confirming that long-memory effects can be modeled in the context of continuous time stationary Markovian processes.

Lobster: The limit order book reconstructor, discussion paper school of business and economics, humboldt universit ̈at zu berlin URL https://lobsterdata.com/LobsterReport.pdf

  • 2011