Large-Sample Properties of Parameter Estimates for Strongly Dependent Stationary Gaussian Time Series
The Annals of Statistics · 1986 · Volume 14 · Issue 2
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.
Keywords
60F99, 62F12, 62M10, fractional ARMA, fractional Gaussian noise, long-range dependence, maximum likelihood estimation, Strong dependence
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