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首页> 外文期刊>Journal of statistical computation and simulation >Accurately sized test statistics with misspecified conditional homoskedasticity
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Accurately sized test statistics with misspecified conditional homoskedasticity

机译：带有错误指定的条件同方差的准确大小的测试统计量

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We study the finite-sample performance of test statistics in linear regression models where the error dependence is of unknown form. With an unknown dependence structure, there is traditionally a trade-off between the maximum lag over which the correlation is estimated (the bandwidth) and the amount of heterogeneity in the process. When allowing for heterogeneity, through conditional heteroskedasticity, the correlation at far lags is generally omitted and the resultant inflation of the empirical size of test statistics has long been recognized. To allow for correlation at far lags, we study the test statistics constructed under the possibly misspecified assumption of conditional homoskedasticity. To improve the accuracy of the test statistics, we employ the second-order asymptotic refinement in Rothenberg [Approximate power functions for some robust tests of regression coefficients, Econometrica 56 (1988), pp. 997-1019] to determine the critical values. The simulation results of this paper suggest that when sample sizes are small, modelling the heterogeneity of a process is secondary to accounting for dependence. We find that a conditionally homoskedastic covariance matrix estimator (when used in conjunction with Rothenberg's second-order critical value adjustment) improves test size with only a minimal loss in test power, even when the data manifest significant amounts of heteroskedasticity. In some specifications, the size inflation was cut by nearly 40% over the traditional heteroskedasticity and autocorrelation consistent (HAC) test. Finally, we note that the proposed test statistics do not require that the researcher specify the bandwidth or the kernel.
机译：我们研究误差依赖性未知的线性回归模型中测试统计数据的有限样本性能。对于未知的依赖关系结构，传统上需要在估计相关性的最大延迟（带宽）与过程中的异质性之间进行权衡。当允许异质性时，通过条件异方差性，通常会忽略远滞后的相关性，并且人们长期以来一直认识到由此产生的检验统计量的经验值膨胀。为了允许在很长的滞后时间进行关联，我们研究在条件同方差的可能错误指定的假设下构建的检验统计量。为了提高检验统计的准确性，我们在Rothenberg中采用了二阶渐近精化法[一些回归系数的鲁棒检验的近似幂函数，Econometrica 56（1988），第997-1019页]，以确定临界值。本文的仿真结果表明，当样本量较小时，对过程的异质性进行建模对于考虑依赖性是次要的。我们发现，有条件的同方差协方差矩阵估计器（当与Rothenberg的二阶临界值调整一起使用时）可以提高测试大小，而测试功率却只有最小的损失，即使数据显示出明显的异方差性也是如此。在某些规范中，与传统的异方差和自相关一致（HAC）测试相比，尺寸膨胀降低了近40％。最后，我们注意到，建议的测试统计数据不需要研究人员指定带宽或内核。

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