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Superstatistical fluctuations in time series of leverage returns

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  • Katz, Y.A.
  • Tian, L.

Abstract

We analyze to what extent the emergence of fat-tailed q-Gaussian distributions of daily leverage returns of North American industrial companies that survive default and de-listing between 2006 and 2012 can be described by superstatistics. To this end, we compare mean values of the Tsallis entropic parameter q obtained by two independent methods: (i) direct fitting of q-Gaussians to distributions of leverage returns; and (ii) derived from shape parameters of Gamma distributions fitted to histograms of inverted realized variances of these returns. For a vast majority of companies, we observe the striking consistency of average values of q obtained by both methods. This finding supports the applicability of superstatistical hypothesis, which assumes that q-Gaussians result from the superposition of locally normal distributions with Gamma-distributed precision (inverted variance).

Suggested Citation

  • Katz, Y.A. & Tian, L., 2014. "Superstatistical fluctuations in time series of leverage returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 405(C), pages 326-331.
    • Handle: RePEc:eee:phsmap:v:405:y:2014:i:c:p:326-331
    DOI: 10.1016/j.physa.2014.03.036
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    References listed on IDEAS

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    1. Flannery, Mark J. & Nikolova, Stanislava (Stas) & Öztekin, Özde, 2012. "Leverage Expectations and Bond Credit Spreads," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 47(4), pages 689-714, August.
    2. Shephard, Neil (ed.), 2005. "Stochastic Volatility: Selected Readings," OUP Catalogue, Oxford University Press, number 9780199257201.
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    2. Xu, Dan & Beck, Christian, 2016. "Transition from lognormal to χ2-superstatistics for financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 453(C), pages 173-183.

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