We propose a simple asymptotic F-distributed Portmanteau test for zero autocorrelations in an otherwise dependent time series. By employing the orthonormal series variance estimator of the variance matrix of sample autocovariances, our test statistic follows an F distribution asymptotically under fixed-smoothing asymptotics. The asymptotic F theory accounts for the estimation error in the underlying variance estimator, which the asymptotic chi-squared theory ignores. Monte Carlo simulations reveal that the F approximation is much more accurate than the corresponding chi-squared approximation in finite samples. Compared with the nonstandard test proposed by Lobato (2001), the asymptotic F test is as easy to use as the chi-squared test: There is no need to obtain critical values by simulations. Further, Monte Carlo simulations indicate that Lobato’s (2001) nonstandard test tends to be heavily undersized under the null and suffers from substantial power loss under the alternatives.

中文翻译：

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存在时间序列相关性时不相关性的渐近 F 检验

我们提出了一个简单的渐近 F 分布 Portmanteau 检验，用于其他相关时间序列中的零自相关。通过使用样本自协方差方差矩阵的正交序列方差估计器，我们的检验统计量在固定平滑渐近下渐近地遵循 F 分布。渐近 F 理论解释了基础方差估计量中的估计误差，而渐近卡方理论忽略了该误差。Monte Carlo 模拟表明，F 近似比有限样本中相应的卡方近似要准确得多。与 Lobato (2001) 提出的非标准检验相比，渐近 F 检验与卡方检验一样易于使用：无需通过模拟获得临界值。更多，