Commonly used tests to assess evidence for the absence of autocorrelation in a univariate time series or serial cross-correlation between time series rely on procedures whose validity holds for i.i.d. data. When the series are not i.i.d., the size of correlogram and cumulative Ljung–Box tests can be significantly distorted. This paper adapts standard correlogram and portmanteau tests to accommodate hidden dependence and nonstationarities involving heteroskedasticity, thereby uncoupling these tests from limiting assumptions that reduce their applicability in empirical work. To enhance the Ljung–Box test for non-i.i.d. data, a new cumulative test is introduced. Asymptotic size of these tests is unaffected by hidden dependence and heteroskedasticity in the series. Related extensions are provided for testing cross-correlation at various lags in bivariate time series. Tests for the i.i.d. property of a time series are also developed. An extensive Monte Carlo study confirms good performance in both size and power for the new tests. Applications to real data reveal that standard tests frequently produce spurious evidence of serial correlation.

用于评估单变量时间序列中不存在自相关或时间序列之间的序列互相关的证据的常用测试依赖于其有效性适用于独立同分布数据的程序。当序列不是独立同分布时，相关图和累积 Ljung-Box 检验的大小可能会显着失真。本文采用标准相关图和组合检验来适应涉及异方差性的隐藏依赖性和非平稳性，从而将这些检验与限制性假设分开，这些假设会降低它们在实证工作中的适用性。为了增强非 iid 数据的 Ljung–Box 检验，引入了新的累积检验。这些检验的渐近大小不受序列中隐藏依赖性和异方差性的影响。提供了相关扩展，用于测试双变量时间序列中各种滞后的互相关。还开发了时间序列 iid 属性的测试。一项广泛的蒙特卡罗研究证实了新测试在尺寸和功率方面的良好性能。对真实数据的应用表明，标准测试经常会产生序列相关性的虚假证据。