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

被引:16
作者
Barboza, Luis A. [1 ]
Viens, Frederi G. [2 ]
机构
[1] Univ Costa Rica, CIMPA, San Jose, Costa Rica
[2] Michigan State Univ, Dept Stat & Probabil, E Lansing, MI 48824 USA
来源
ELECTRONIC JOURNAL OF STATISTICS | 2017年 / 11卷 / 01期
基金
美国国家科学基金会;
关键词
Fractional Brownian motion; Ornstein Uhlenbeck process; method of moments; CENTRAL LIMIT-THEOREMS; LARGE-SAMPLE PROPERTIES; QUADRATIC VARIATIONS; MALLIAVIN CALCULUS; LONG-MEMORY; DISCRETE; INDEX; TIME;
D O I
10.1214/17-EJS1230
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
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 data-points is moderate.
引用
收藏
页码:401 / 439
页数:39
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