Superstatistical fluctuations in time series of leverage returns

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).