A wavelet analysis of the Rosenblatt process: chaos expansion and estimation of the self-similarity parameter
arXiv:0811.2664 · doi:10.1016/j.spa.2010.08.003
Abstract
By using chaos expansion into multiple stochastic integrals, we make a wavelet analysis of two self-similar stochastic processes: the fractional Brownian motion and the Rosenblatt process. We study the asymptotic behavior of the statistic based on the wavelet coefficients of these processes. Basically, when applied to a non-Gaussian process (such as the Rosenblatt process) this statistic satisfies a non-central limit theorem even when we increase the number of vanishing moments of the wavelet function. We apply our limit theorems to construct estimators for the self-similarity index and we illustrate our results by simulations.
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- On a class of self-similar processes with stationary increments in higher order Wiener chaoses
- Large scale behavior of wavelet coefficients of non-linear subordinated processes with long memory
- Convergence Rate Analysis in Limit Theorems for Nonlinear Functionals of the Second Wiener Chaos
- Variations and Hurst index estimation for a Rosenblatt process using longer filters