Parameter Estimation of Gaussian Stationary Processes using the Generalized Method of Moments
Statistics Theory
2017-01-18 v2 Statistics Theory
Abstract
We consider the class of all stationary Gaussian process with explicit parametric spectral density. Under some conditions on the autocovariance function, we defined a GMM estimator that satisfies consistency and asymptotic normality, using the Breuer-Major theorem and previous results on ergodicity. This result is applied to the joint estimation of the three parameters of a stationary Ornstein-Uhlenbeck (fOU) process driven by a fractional Brownian motion. The asymptotic normality of its GMM estimator applies for any H in (0,1) and under some restrictions on the remaining parameters. A numerical study is performed in the fOU case, to illustrate the estimator's practical performance when the number of datapoints is moderate.
Keywords
Cite
@article{arxiv.1604.06511,
title = {Parameter Estimation of Gaussian Stationary Processes using the Generalized Method of Moments},
author = {Luis A. Barboza and Frederi G. Viens},
journal= {arXiv preprint arXiv:1604.06511},
year = {2017}
}