Dahlhaus, Rainer Efficient parameter estimation for self-similar processes. (English) Zbl 0703.62091 Ann. Stat. 17, No. 4, 1749-1766 (1989). 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 Cited in 4 ReviewsCited in 182 Documents MSC: 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 Keywords:fractional ARMA; Asymptotic normality; maximum likelihood estimator; long range dependent Gaussian process; limit of the Fisher information matrix; efficiency; approximate maximum likelihood estimator; asymptotic properties of Toeplitz matrices; equicontinuity property of quadratic forms Citations:Zbl 0606.62096 PDF BibTeX XML Cite \textit{R. Dahlhaus}, Ann. Stat. 17, No. 4, 1749--1766 (1989; Zbl 0703.62091) Full Text: DOI OpenURL