Surrogate analysis of volatility series from long-range correlated noise

Detrended fluctuation analysis (DFA) [C.-K. Peng, S.V. Buldyrev, A.L. Goldberger, S. Havlin, F. Sciortino, M. Simons, H.E. Stanley, Nature 356 (1992) 168] of volatility series has been proposed to identify possible nonlinear/multifractal signatures in the given empirical sample [Y. Ashkenazy, P.Ch. Ivanov, S. Havlin, C.-K. Peng, A.L. Goldberger, H.E. Stanley, Phys. Rev. Lett. 86 (2001) 1900; Y. Ashkenazy, S. Havlin, P. Ch. Ivanov, C.-K. Peng, V. Schulte-Frohlinde, H.E. Stanley, Physica A. 323 (2003) 19; T. Kalisky, Y. Ashkenazy, S. Havlin, Phys. Rev. E 72 (2005) 011913]. Long-range volatility 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 [Y. Ashkenazy, P.Ch. Ivanov, S. Havlin, C.-K. Peng, A.L. Goldberger, H.E. Stanley, Phys. Rev. Lett. 86 (2001) 1900; Y. Ashkenazy, S. Havlin, P. Ch. Ivanov, C.-K. Peng, V. Schulte-Frohlinde, H.E. Stanley, Physica A. 323 (2003) 19; T. Kalisky, Y. Ashkenazy, S. Havlin, Phys. Rev. E 72 (2005) 011913]. In this brief communication, surrogate testing of volatility series from long-range correlated monofractal noise and their static, invertible nonlinear transforms is investigated. Long-range correlated noise is generated from fractional auto regressive integrated moving average (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 analysis of volatility series in the presence of non-Gaussian innovations.