ON SIZE AND POWER OF HETEROSKEDASTICITY AND AUTOCORRELATION ROBUST TESTS
ON SIZE AND POWER OF HETEROSKEDASTICITY AND AUTOCORRELATION ROBUST TESTS
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DOI：
10.1017/s0266466614000899
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发表时间：
2013-04
影响因子：
0.8
通讯作者：
David Preinerstorfer;B. M. Pötscher
中科院分区：
文献类型：
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作者：
David Preinerstorfer;B. M. Pötscher
测试线性模型中回归系数的限制通常需要针对干扰之间潜在的异方差或自相关校正传统的 F 检验，从而产生所谓的异方差和自相关鲁棒测试程序。开发这些程序的目的是减弱未校正 F 检验中存在的尺寸扭曲和功效不足。我们开发了一种通用理论来建立关于一大类异方差和自相关稳健检验的大小和功效属性的正和负有限样本结果。使用这些结果，我们表明，在协方差模型的非常弱的假设和设计矩阵的一般条件下，具有平稳扰动的时间序列回归模型中的非参数和参数校正的 F 型检验的大小要么等于 1，要么无益无穷幂等于 0。此外，我们建议基于人工回归的调整程序。这种调整解决了许多情况下的问题，因为如此调整的测试不会受到尺寸扭曲的影响。同时，它们的幂函数远离零。作为第二个应用，我们讨论异方差扰动的情况。
Testing restrictions on regression coefficients in linear models often requires correcting the conventional F-test for potential heteroskedasticity or autocorrelation amongst the disturbances, leading to so-called heteroskedasticity and autocorrelation robust test procedures. These procedures have been developed with the purpose of attenuating size distortions and power deficiencies present for the uncorrected F-test. We develop a general theory to establish positive as well as negative finite-sample results concerning the size and power properties of a large class of heteroskedasticity and autocorrelation robust tests. Using these results we show that nonparametrically as well as parametrically corrected F-type tests in time series regression models with stationary disturbances have either size equal to one or nuisance-infimal power equal to zero under very weak assumptions on the covariance model and under generic conditions on the design matrix. In addition we suggest an adjustment procedure based on artificial regressors. This adjustment resolves the problem in many cases in that the so-adjusted tests do not suffer from size distortions. At the same time their power function is bounded away from zero. As a second application we discuss the case of heteroskedastic disturbances.