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

TL;DR

This paper investigates whether non-Gaussian innovations in linear feedback processes can generate long-range correlations in volatility series, finding that non-Gaussianity alone may be sufficient for such correlations.

Contribution

It demonstrates that non-Gaussian innovations can produce long-range volatile correlations in stationary linear processes, unlike Gaussian innovations.

Findings

Gaussian innovations show uncorrelated volatility behavior

Non-Gaussian innovations exhibit significant long-range correlations

Non-Gaussianity may be sufficient for long-range volatility correlations

Abstract

Scaling analysis of the magnitude series (volatile series) has been proposed recently to identify possible nonlinear/multifractal signatures in the given data [1-3]. In this letter, 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.