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

Dahlhaus, Rainer

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

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