SECOND ORDER EXPANSION OF THET-STATISTIC IN AR(1) MODELS
在局部单位根渐近框架下推导了AR(1)模型t统计量的二阶展开，并证明非参数网格自助法相比网格检验法能达到二阶改进，对从事单位根检验和置信区间构造的计量经济学研究者有参考价值。
The purpose of this paper is to differentiate between several asymptotically valid methods for confidence set construction for the autoregressive coefficient in AR(1) models. We show that the nonparametric grid bootstrap procedure suggested by Hansen (1999, Review of Economics and Statistics 81, 594–607) achieves a second order refinement in the local-to-unity asymptotic approach when compared with a modified version of Stock’s (1991, Journal of Monetary Economics 28, 435–459) and Andrews’ (1993, Econometrica 61, 139–165) grid testing procedures. We establish a second order expansion of the t -statistic in an AR(1) model in the local-to-unity asymptotic approach, which differs drastically from the usual Edgeworth-type expansions by approximating the statistic around a nonstandard and nonpivotal limit.