Mathematics – Statistics Theory
Scientific paper
2012-04-19
Mathematics
Statistics Theory
45 pages, 3 figures
Scientific paper
In this paper, we propose a class of estimators for estimating the asymptotic covariance matrix of the generalized method of moments estimator in the stationary time series models. Our proposal provides a unification of the existing smoothing parameter dependent covariance estimators, including the traditional heteroskedasticity and autocorrelation consistent covariance estimator and some recently developed estimators, such as cluster-based covariance estimator and projection-based covariance estimator. Under mild conditions, we establish the first order asymptotic distribution for the Wald statistics when the smoothing parameter is held fixed. Furthermore, we derive higher order Edgeworth expansions for the finite sample distribution of the Wald statistics in the Gaussian location model under the fixed-smoothing paradigm. In particular, we show that the error of asymptotic approximation is at the order of the reciprocal of the sample size and obtain explicit forms for the leading error terms in the expansions. The results are used to justify the second order correctness of a new bootstrap method, the Gaussian dependent bootstrap, in the context of Gaussian location model. Some simulation results are also presented to corroborate our theoretical findings.
Shao Xiaofeng
Zhang Xianyang
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