Is non-Gaussianity sufficient to produce long-range volatile correlations?

Scaling analysis of the magnitude series (volatile series) has been proposed recently to identify possible non-linear/multifractal signatures in the given data [Y. Ashkenazy, et al. Phys. Rev. Lett. 86 (2001) 1900; Y. Ashkenazy, et al. Physica A 323 (2003) 19; T. Kalisky, Y. Ashkenazy, S. Havlin. Phys. Rev. E 72 (2005) 011913]. In this article, correlations of volatile series generated from stationary first-order linear feedback process with Gaussian and non-Gaussian innovations are investigated. While volatile correlations corresponding to Gaussian innovations exhibited uncorrelated behavior across all time scales, those of non-Gaussian innovations showed significant deviation from uncorrelated behavior even at large time scales. The results presented raise the intriguing question whether non-Gaussian innovations can be sufficient to realize long-range volatile correlations.