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Systems with Correlations in the Variance: Generating Power-Law Tails in Probability Distributions

Boris Podobnik·Plamen Ch. Ivanov·Youngki Lee·Alessandro Chessa·H. Eugene Stanley
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Abstract

We study how the presence of correlations in physical variables contributes to the form of probability distributions. We investigate a process with correlations in the variance generated by (i) a Gaussian or (ii) a truncated Lévy distribution. For both (i) and (ii), we find that due to the correlations in the variance, the process ``dynamically'' generates power-law tails in the distributions, whose exponents can be controlled through the way the correlations in the variance are introduced. For (ii), we find that the process can extend a truncated distribution {\it beyond the truncation cutoff}, which leads to a crossover between a Lévy stable power law and the present ``dynamically-generated'' power law. We show that the process can explain the crossover behavior recently observed in the $S&P500$ stock index.

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Boris Podobnik, Plamen Ch. Ivanov, Youngki Lee, Alessandro Chessa, H. Eugene Stanley. 2000-05-08. Systems with Correlations in the Variance: Generating Power-Law Tails in Probability Distributions. https://doi.org/10.1209/epl%2Fi2000-00540-7

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