Fixed-Smoothing Asymptotics for Time Series

• Activity Number: 352
• Type: Contributed
• Date/Time: Tuesday, August 2, 2011 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Xianyang Zhang*+ and Xiaofeng Shao
• Companies: University of Illinois at Urbana-Champaign and University of Illinois at Urbana-Champaign
• Keywords: Fixed-smoothing ; generalized method of moments ; High order expansion ; Long run variance

Abstract

This paper proposes a wide class of estimators for estimating the asymptotic covariance matrix of the GMM (generalized method of moments) estimator in the stationary time series models. The proposed estimator is general enough to include the traditional heteroskedasticity and autocorrelation consistent covariance estimatior and some recent developed estimators, such as cluster covariance estimator and projection-based covariance estimator, as special cases. Under the framework of Gaussian location model, we derive a high order expansion for the corresponding Wald statistic when the underlying smoothing parameter is held fixed. Specifically, we show that the error rejection probability is of order $O(1/T)$, where $T$ is the sample size, and derive the leading term in the expansion under the fixed-smoothing asymptotics. Furthermore, we propose a novel bootstrap method, called Gaussian dependent bootstrap, and show that the bootstrap based inference is more accurate than the first order approximation.