论文标题
测试GARCH-X类型模型时允许识别较弱
Allowing for weak identification when testing GARCH-X type models
论文作者
论文摘要
在本文中，我们在Andrews and Cheng（2012）中使用结果，该结果扩展为允许参数在参数空间的附近或边界处，从而得出了由Pedersen和Rahbek（2019）提出的两步（测试）过程中两个测试统计量的渐近分布。后者旨在测试零假设，即具有外源协变量（x）的GARCH-X型模型还原为标准的GARCH型模型，同时允许“ GARCH参数”被识别。然后，我们为任何测试的渐近大小提供了检验该零假设的渐近大小，然后在数值上建立了在5％名义水平的两步过程的渐近大小上的下限。该下限超过了标称水平，表明两步过程无法控制渐近尺寸。在一项模拟研究中，我们表明该发现与有限样本有关，因为两步程序可能会在有限样本中过度拒绝。我们还提出了一项新测试，该测试通过构造控制渐近尺寸，并且发现“ Arch参数”为“非常小”时，发现比两步过程更强大（在这种情况下，两步过程不足的估算不足）。
In this paper, we use the results in Andrews and Cheng (2012), extended to allow for parameters to be near or at the boundary of the parameter space, to derive the asymptotic distributions of the two test statistics that are used in the two-step (testing) procedure proposed by Pedersen and Rahbek (2019). The latter aims at testing the null hypothesis that a GARCH-X type model, with exogenous covariates (X), reduces to a standard GARCH type model, while allowing the "GARCH parameter" to be unidentified. We then provide a characterization result for the asymptotic size of any test for testing this null hypothesis before numerically establishing a lower bound on the asymptotic size of the two-step procedure at the 5% nominal level. This lower bound exceeds the nominal level, revealing that the two-step procedure does not control asymptotic size. In a simulation study, we show that this finding is relevant for finite samples, in that the two-step procedure can suffer from overrejection in finite samples. We also propose a new test that, by construction, controls asymptotic size and is found to be more powerful than the two-step procedure when the "ARCH parameter" is "very small" (in which case the two-step procedure underrejects).
