Surrogate testing of volatility series from long-range correlated noise

Abstract

Detrended fluctuation analysis (DFA) [1] of the volatility series has been found to be useful in dentifying possible nonlinear/multifractal dynamics in the empirical sample [2-4]. Long-range volatile correlation can be an outcome of static as well as dynamical nonlinearity. In order to argue in favor of dynamical nonlinearity, surrogate testing is used in conjunction with volatility analysis [2-4]. In this brief communication, surrogate testing of volatility series from long-range correlated noise and their static, invertible nonlinear transforms is investigated. Long-range correlated monofractal noise is generated using FARIMA (0, d, 0) with Gaussian and non-Gaussian innovations. We show significant deviation in the scaling behavior between the empirical sample and the surrogate counterpart at large time-scales in the case of FARIMA (0, d, 0) with non-Gaussian innovations whereas no such discrepancy was observed in the case of Gaussian innovations. The results encourage cautious interpretation of surrogate testing in the presence of non-Gaussian innovations.