Asymptotic behavior of the Whittle estimator for the increments of a Rosenblatt process

TL;DR

This paper investigates the asymptotic properties of the Whittle estimator when used to estimate the self-similarity index of the Rosenblatt process, demonstrating a non-central limit theorem and supporting findings with simulations.

Contribution

It provides the first analysis of the Whittle estimator's asymptotic behavior for the Rosenblatt process, including a non-central limit theorem derivation.

Findings

Establishment of a non-central limit theorem for the estimator

Numerical simulations confirming theoretical results

Insights into the estimator's asymptotic distribution

Abstract

The purpose of this paper is to estimate the self-similarity index of the Rosenblatt process by using the Whittle estimator. Via chaos expansion into multiple stochastic integrals, we establish a non-central limit theorem satisfied by this estimator. We illustrate our results by numerical simulations.