Best attainable rates of convergence for the estimation of the memory parameter

Details Best attainable rates of convergence for the estimation of the memory parameter Best attainable rates of convergence for the estimation of the memory parameter

2009-05-31

arxiv.org/abs/0906.0180v1

Dependence in Probability and Statistics, Paul Doukhan, Gabriel Lang, Donatas Surgailis and Gilles Teyssi\`ere (Ed.) (2010) 45

Mathematics

Statistics Theory

Scientific paper

10.1007/978-3-642-14104-1

The purpose of this note is to prove a lower bound for the estimation of the memory parameter of a stationary long memory process. The memory parameter is defined here as the index of regular variation of the spectral density at 0. The rates of convergence obtained in the literature assume second order regular variation of the spectral density at zero. In this note, we do not make this assumption, and show that the rates of convergence in this case can be extremely slow. We prove that the log-periodogram regression (GPH) estimator achieves the optimal rate of convergence for Gaussian long memory processes.

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