Considerable evidence in past research shows size distortion in standard tests for zero autocorrelation or zero cross-correlation when time series are not independent identically distributed random variables, pointing to the need for more robust procedures. Recent tests for serial correlation and cross-correlation in Dalla, Giraitis, and Phillips (2022) provide a more robust approach, allowing for heteroskedasticity and dependence in uncorrelated data under restrictions that require a smooth, slowly-evolving deterministic heteroskedasticity process. The present work removes those restrictions and validates the robust testing methodology for a wider class of innovations and regression residuals allowing for heteroscedastic uncorrelated and non-stationary data settings. The updated analysis given here enables more extensive use of the methodology in practical applications. Monte Carlo experiments confirm excellent finite sample performance of the robust test procedures even for extremely complex white noise processes. The empirical examples show that use of robust testing methods can materially reduce spurious evidence of correlations found by standard testing procedures.

中文翻译：

---

一般异质性下相关性的稳健推断

过去研究中的大量证据表明，当时间序列不是独立同分布的随机变量时，零自相关或零互相关的标准测试中会出现大小失真，这表明需要更稳健的程序。Dalla、Giraitis 和 Phillips (2022) 最近对序列相关和互相关的测试提供了一种更稳健的方法，允许在需要平滑、缓慢演变的确定性异方差过程的限制下，实现不相关数据的异方差和依赖性。目前的工作消除了这些限制，并验证了更广泛类别的创新和回归残差的稳健测试方法，允许异方差不相关和非平稳数据设置。这里给出的更新分析使得该方法能够在实际应用中得到更广泛的使用。蒙特卡洛实验证实，即使对于极其复杂的白噪声过程，鲁棒测试程序也具有出色的有限样本性能。经验例子表明，使用稳健的测试方法可以大大减少标准测试程序发现的相关性的虚假证据。