Research in Econometric Methods

该提案描述了对几个新专题的研究以及在几个领域中继续进行的研究。首先，PI将考虑长记忆参数‘d’的减少偏差的半参数估计。这一参数最常见的估计量，Geweke and Porter-Hudak(GPH)估计量，已被发现具有相当大的有限样本偏差。PI和耶鲁大学研究生P.Guggenberger将开发另一种GPH估计器，其偏差减少一个数量级，其方差仅增加一个乘法常数，其收敛速度比GPH估计器更快。当归一化谱密度是S阶的零光滑性时，我们计划建立‘d’估计的最优收敛速度，并证明了去偏GPH估计达到这个速度，但对于S 2，GPH估计不能达到这个速度。PI将与耶鲁大学研究生孙艺晓合作开发一种局部多项式白估计，它的行为与其他局部白估计相似，但具有更少的偏差和更快的收敛速度。第二个拟议的研究领域是关于非线性估计的自举。这项研究继续了PI已经报道的工作。我们的目标是获得对Bootstrapping最小距离估计和间接推断估计的高阶改进，IID非参数Bootstrap比现有结果更强的高阶改进结果，以及基于残差和BCA的Bootstrap以及Lagrange乘子(LM)和似然比(LR)检验的新结果。第三个研究领域是发展经典LM、LR和Wald检验的一些新的渐近最优性。我们的想法是推广这样的发现，即针对AR(1)误差的序列相关性的LM检验与针对MA(1)误差的检验是相同的。这一发现表明，对于AR(1)和MA(1)误差的检验，LM、LR和Wald检验都具有Wald-型渐近最优性。这种类型的结果更普遍地适用于这个模型和许多其他模型。研究的目的是得到一些一般性的结果，以确定不同类别的备选模型对于给定的LM、LR或Wald检验具有渐近最优性。第四个研究领域继续了PI关于参数在维持假设的边界上且参数出现在备选模型下而不是零假设下的检验问题的研究。这类问题的例子已经很多了，我们相信随着研究人员越来越多地依赖于非线性模型，这类问题将变得越来越普遍。我们的目的是证明LR、LM和Wald检验是渐近可容许的，发展了对某些权函数最大化加权平均功率的新检验，构造了一类完备的检验，并建立了马尔可夫制度转换模型中LR、LM和Wald检验的渐近零分布。最后，我们计划证明用于检验GARCH(1，1)形式的条件异方差的LR、LM和Wald检验对于任何形式的序列相关在平方误差中是一致的。

This proposal describes research on several new topics and continued research in several areas. First, the PI will consider bias-reduced semiparametric estimation of the long memory parameter 'd'. The most common estimator of this parameter, the Geweke and Porter-Hudak (GPH) estimator, has been found to have substantial finite sample bias. The PI and P. Guggenberger, a graduate student at Yale, will develop an alternative GPH estimator whose bias is reduced by an order of magnitude, whose variance is increased only by a multiplicative constant, and whose rate of convergence is faster than that of the GPH estimator. We plan to establish the optimal rate of convergence of estimators of 'd' when the normalized spectral density is smooth of order s at zero and show that the bias-reduced GPH estimator attains this rate, but, for s 2, the GPH estimator does not. Working with Yixiao Sun, a graduate student at Yale, the PI will develop a local polynomial Whittle estimator that behaves like other local Whittle estimators, but has reduced bias and a faster rate of convergence.The second area of proposed research is on the bootstrap for nonlinear estimators. This research continues work already reported by the PI.. We aim to obtain higher-order improvements for bootstrapping minimum distance and indirect inference estimators, stronger higher-order improvement results for the iid nonparametric bootstrap than those currently available, and new results for residual-based and BCa bootstraps and Lagrange multiplier (LM) and likelihood ratio (LR) tests.The third area of research is to develop some new asymptotic optimality properties of the classical LM, LR, and Wald tests. The idea is to generalize the finding that the LM test for serial correlation against AR(1) errors is the same as that against MA(1) errors. This finding implies that the LM, LR, and Wald tests have Wald-type asymptotic optimality properties for testing against both AR(1) and MA(1) errors. Results of this type hold more generally, both in this model and in many other models. The object of the proposed research is to obtain some general results that determine different classes of alternative models for which a given LM, LR, or Wald test has asymptotic optimality properties.The fourth area of proposed research continues the PI's research on testing problems when a parameter is on the boundary of the maintained hypothesis and a parameter appears under the alternative but not under the null hypothesis. Numerous examples of such problems already exist, and we believe that problems of this sort will become increasingly prevalent as researchers rely more and more on nonlinear models. We aim to show that the LR, LM, and Wald tests are asymptotically admissible, develop new tests that maximize weighted average power for certain weight functions, construct a complete class of tests, and establish the asymptotic null distribution of the LR, LM, and Wald tests in the Markov regime switching model. Finally, we plan to show that the LR, LM, and Wald tests for testing for conditional heteroskedasticity of GARCH(1, 1) form are consistent against any form of serial correlation in the squared errors.