Efficient parameter estimation for self-similar processes. (English) Zbl 0703.62091

Asymptotic normality of the maximum likelihood estimator for the parameters of a long range dependent Gaussian process is proved. Furthermore, the limit of the Fisher information matrix is derived for such processes, which implies efficiency of the estimator and of an approximate maximum likelihood estimator studied by R. Fox and M. S. Taqqu [ibid. 14, 517-532 (1986; Zbl 0606.62096)]. The results are derived by using asymptotic properties of Toeplitz matrices and an equicontinuity property of quadratic forms.
Reviewer: H.Strasser


62M09 Non-Markovian processes: estimation
62F12 Asymptotic properties of parametric estimators
60F99 Limit theorems in probability theory
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62E20 Asymptotic distribution theory in statistics


Zbl 0606.62096
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