## The Annals of Statistics

### Large-Sample Properties of Parameter Estimates for Strongly Dependent Stationary Gaussian Time Series

#### Abstract

A strongly dependent Gaussian sequence has a spectral density $f(x, \theta)$ satisfying $f(x, \theta) \sim |x|^{-\alpha(\theta)} L_\theta(x)$ as $x \rightarrow 0$, where $0 < \alpha(\theta) < 1$ and $L_\theta(x)$ varies slowly at 0. Here $\theta$ is a vector of unknown parameters. An estimator for $\theta$ is proposed and shown to be consistent and asymptotically normal under appropriate conditions. These conditions are satisfied by fractional Gaussian noise and fractional ARMA, two examples of strongly dependent sequences.

#### Article information

Source
Ann. Statist., Volume 14, Number 2 (1986), 517-532.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176349936

Digital Object Identifier
doi:10.1214/aos/1176349936

Mathematical Reviews number (MathSciNet)
MR840512

Zentralblatt MATH identifier
0606.62096

JSTOR