Variations and estimators for self-similarity parameters via Malliavin calculus

Tudor, Ciprian A.; Viens, Frederi G.

Ann. Probab., Tome 37 (2009) no. 1, p. 2093-2134 / Harvested from Project Euclid

Résumé

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∈(1/2, 2/3).

Publié le : 2009-11-15
Classification: Multiple stochastic integral, Hermite process, fractional Brownian motion, Rosenblatt process, Malliavin calculus, noncentral limit theorem, quadratic variation, Hurst parameter, self-similarity, statistical estimation, 60F05, 60H05, 60G18, 62F12

@article{1258380783,
     author = {Tudor, Ciprian A. and Viens, Frederi G.},
     title = {Variations and estimators for self-similarity parameters via Malliavin calculus},
     journal = {Ann. Probab.},
     volume = {37},
     number = {1},
     year = {2009},
     pages = { 2093-2134},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258380783}
}

Tudor, Ciprian A.; Viens, Frederi G. Variations and estimators for self-similarity parameters via Malliavin calculus. Ann. Probab., Tome 37 (2009) no. 1, pp.  2093-2134. http://gdmltest.u-ga.fr/item/1258380783/