On discrete stochastic processes with long-lasting time dependence

Silvio M. Duarte Queiros

Papers from arXiv.org

Abstract: 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.

Date: 2008-06, Revised 2009-01
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Published in Eur. Phys. J. B 66, 137-148 (2008)

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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:0806.2617

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