## Electronic Journal of Statistics

### Parameter estimation of Gaussian stationary processes using the generalized method of moments

#### 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.

#### Article information

Source
Electron. J. Statist., Volume 11, Number 1 (2017), 401-439.

Dates
First available in Project Euclid: 20 February 2017

https://projecteuclid.org/euclid.ejs/1487581428

Digital Object Identifier
doi:10.1214/17-EJS1230

Mathematical Reviews number (MathSciNet)
MR3611508

Zentralblatt MATH identifier
06702349

#### Citation

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

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