Research in Econometric Methods

该提案介绍了对若干新课题的研究以及在若干领域继续开展的研究。 首先，PI将考虑长记忆参数“d”的偏倚减少的半参数估计。这个参数的最常见的估计，Geweke和Porter-Hudak（GPH）估计，已被发现有很大的有限样本偏差。PI和耶鲁大学的研究生P. Guggenberger将开发另一种GPH估计量，其偏差降低了一个数量级，其方差仅增加了一个乘法常数，并且其收敛速度比GPH估计量更快。我们计划建立最佳的收敛速度的估计'd'时，归一化的谱密度是光滑的顺序S在零，并表明，减少偏见的GPH估计达到这个速度，但是，对于S 2，GPH估计不。PI将与耶鲁大学的研究生Yixiao Sun合作，开发一种局部多项式Whittle估计，其行为与其他局部Whittle估计类似，但具有更小的偏差和更快的收敛速度。拟议研究的第二个领域是非线性估计的自助法。这项研究继续了PI已经报告的工作。我们的目标是获得bootstrapping最小距离估计和间接推断估计的高阶改进，iid非参数bootstrapping估计的高阶改进结果，以及基于残差和BCa bootstrapping估计以及拉格朗日乘子（LM）和似然比（LR）检验的新结果。Wald测试这个想法是推广的发现，对AR（1）错误的序列相关性的LM测试是相同的对MA（1）错误。这一发现意味着LM、LR和Wald检验对于AR（1）和MA（1）误差都具有Wald型渐近最优性。这种类型的结果在这个模型和许多其他模型中更普遍地成立。建议的研究的目的是获得一些一般性的结果，确定不同类别的替代模型，其中一个给定的LM，LR，或Wald测试具有渐近最优properties.第四个领域的建议的研究继续PI的研究测试问题时，一个参数是在边界上的维持假设和一个参数下出现的替代，但不是根据零假设。 这样的问题已经存在了许多例子，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。我们的目标是证明LR，LM和Wald测试是渐近容许的，开发新的测试，最大化加权平均功率为某些权重函数，构建一个完整的测试类，并建立渐近零分布的LR，LM和Wald测试在马尔可夫状态转换模型。 最后，我们计划表明，LR，LM，和Wald测试的条件异方差的Gestival（1，1）形式的测试是一致的，对任何形式的序列相关的平方误差。

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.