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Abstract: Using multiple stochastic integrals and the Malliavin calculus, we analyzethe asymptotic behavior of quadratic variations for a specific non-Gaussianself-similar process, the Rosenblatt process. We apply our results to thedesign of strongly consistent statistical estimators for the self-similarityparameter $H$. Although, in the case of the Rosenblatt process, our estimatorhas non-Gaussian asymptotics for all $H>1-2$, we show the remarkable fact thatthe process-s data at time 1 can be used to construct a distinct, compensatedestimator with Gaussian asymptotics for $H\in1-2,2-3$.



Author: Ciprian Tudor CES, SAMOS, Frederi Viens

Source: https://arxiv.org/



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