We establish sufficient conditions on durations that are stationary with finite variance and memory parameter d 2 [0; 1=2) to ensure that the corresponding counting process N(t) satisfies VarN(t) raquo; Ct2d+1 (C gt; 0) as t ! 1, with the same memory parameter d 2 [0; 1=2) that was assumed for the...

We discuss some of the issues pertaining to modelling and estimating long memory in volatility. Themain focus is on semi parametric estimation of the memory parameter in the long memory stochasticvolatility model. We present the asymptotic properties of the log periodogram regression estimator...