Electronic Journal of Statistics
- Electron. J. Statist.
- Volume 11, Number 1 (2017), 401-439.
Parameter estimation of Gaussian stationary processes using the generalized method of moments
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.
Electron. J. Statist., Volume 11, Number 1 (2017), 401-439.
Received: April 2016
First available in Project Euclid: 20 February 2017
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Barboza, Luis A.; Viens, Frederi G. Parameter estimation of Gaussian stationary processes using the generalized method of moments. Electron. J. Statist. 11 (2017), no. 1, 401--439. doi:10.1214/17-EJS1230. https://projecteuclid.org/euclid.ejs/1487581428