On discrete stochastic processes with long-lasting time dependence

Details On discrete stochastic processes with long-lasting time dependence On discrete stochastic processes with long-lasting time dependence

2008-06-16

arxiv.org/abs/0806.2617v2

Eur. Phys. J. B 66, 137-148 (2008)

Physics

Data Analysis, Statistics and Probability

24 pages

Scientific paper

10.1140/epjb/e2008-00387-2

In this manuscript, we analytically and numerically study statistical properties of an heteroskedastic process based on the celebrated ARCH generator of random variables whose variance is defined by a memory of $q_{m}$-exponencial, form ($e_{q_{m}=1}^{x}=e^{x}$). Specifically, we inspect the self-correlation function of squared random variables as well as the kurtosis. In addition, by numerical procedures, we infer the stationary probability density function of both of the heteroskedastic random variables and the variance, the multiscaling properties, the first-passage times distribution, and the dependence degree. Finally, we introduce an asymmetric variance version of the model that enables us to reproduce the so-called leverage effect in financial markets.

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