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

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.

10 pages, 7 figures

References in corpus (10)

• Markov Processes, Hurst Exponents, and Nonlinear Diffusion Equations with application to finance
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• Detrended cross-correlations between returns, volatility, trading activity, and volume traded for the stock market companies
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• Three-state herding model of the financial markets
• Trading activity as driven Poisson process: comparison with empirical data
• Long-range memory model of trading activity and volatility
• Nonlinear GARCH model and 1/f noise
• Interplay between endogenous and exogenous fluctuations in financial markets

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