Before revision: Using theory on (conditionally) Gaussian processes with stationary increments developed in Barndorff-Nielsen et al. (2009, 2011), this paper presents a general semiparametric approach to conducting inference on the fractal index , \alpha, of a time series. Our setup encompasses a large class of Gaussian processes and we show how to extend it to a large class of non-Gaussian models as well.
After revision: Using theory on (conditionally) Gaussian processes with stationary increments developed in Barndorff-Nielsen et al. (2009, 2011), this paper presents a general semiparametric approach to conducting inference on the fractal index of a stochastic process. Our framework is very general and encompasses many models of interest; we show how to extend it to a large class of non-Gaussian models as well.