Parameter estimation in long-memory and other Gaussian processes

Frederi Viens, Department of Statistics & Probability, Michigan State University, USA

We consider the class of all stationary Gaussian processes. When the spectral density is parametrically explicit, we defined a Generalized Method of Moments estimator that satisfies consistency and asymptotic normality, using the Breuer-Major theorem which applies to long-memory processes. This result is applied to the joint estimation of the three parameters of a stationary fractional Ornstein-Uhlenbeck (fOU) process driven for all Hurst parameters. For general processes observed at fixed discrete times, no matter what the memory length, we use state-of-the-art Malliavin calculus tools to prove Berry-Esseen-type and other speeds of convergence in total variation, for estimators based on power variations. This is joint work with Luis Barboza (U. Costa Rica), Khalifa es-Sebaiy (U. Kuwait), and Soukaina Douissi (U. Cadi Ayyad, Morocco).

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