Application of Malliavin calculus to long-memory parameter estimation for non-Gaussian processes

Abstract

Using multiple Wiener–Itô stochastic integrals and Malliavin calculus we study the rescaled quadratic variations of a general Hermite process of order q with long-memory (Hurst) parameter H ∈ ( 1 2 , 1 ) . We apply our results to the construction of a strongly consistent estimator for H. It is shown that the estimator is asymptotically non-normal, and converges in the mean-square, after normalization, to a standard Rosenblatt random variable. To cite this article: A. Chronopoulou et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009).