文章基本信息

标题：Parameter estimation of Gaussian stationary processes using the generalized method of moments
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作者：Luis A. Barboza ; Frederi G. Viens
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2017
卷号：11
期号：1
页码：401-439
DOI：10.1214/17-EJS1230
语种：English
出版社：Institute of Mathematical Statistics
摘要：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.
关键词：Fractional Brownian motion;Ornstein Uhlen beck process;method of moments.