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

V. Gontis, A. Kononovicius

posted on 06 January 2017

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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.


There is a fundamental problem to empirically establish which of the possible alternatives, fBm or stochastic processes with non-stationary increments, is most well-suited to describe long-range memory in the financial markets. The main idea is to employ the dependence of first passage time PDF on Hurst parameter H for the fBm.