VARIATIONS AND ESTIMATORS FOR SELF-SIMILARITY PARAMETERS VIA MALLIAVIN CALCULUS

Using multiple stochastic integrals and the Malliavin calculus, we analyze the asymptotic behavior of quadratic variations for a specific non-Gaussian self-similar process, the Rosenblatt process. We apply our results to the design of strongly consistent statistical estimators for the self-similarity parameter H. Although, in the case of the Rosenblatt process, our estimator has non-Gaussian asymptotics for all H > 1/2, we show the remarkable fact that the process’s data at time 1 can be used to construct a distinct, compensated estimator with Gaussian asymptotics for H 2 (1/2,2/3).