Asymptotic behavior of the Whittle estimator for the increments of a Rosenblatt process. (English) Zbl 1298.60045
Summary: The purpose of this paper is the estimation of 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.
MSC:
| 60G18 | Self-similar stochastic processes |
| 60F05 | Central limit and other weak theorems |
| 60H05 | Stochastic integrals |
| 62F12 | Asymptotic properties of parametric estimators |
Keywords:
Whittle estimator; Rosenblatt process; long-memory process; non-central limit theorem; multiple Wiener-Itô integralsSoftware:
longmemoReferences:
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