Testing cross-sectional independence in panel data models is of fundamental importance in econometric analysis with high-dimensional panels. Recently, econometricians began to turn their attention to the problem in the presence of serial dependence. The existing procedure for testing cross-sectional independence with serial correlation is based on the sum of the sample cross-sectional correlations, which generally performs well when the alternative has dense cross-sectional correlations, but suffers from low power against sparse alternatives. To deal with sparse alternatives, we propose a test based on the maximum of the squared sample cross-sectional correlations. Furthermore, we propose a combined test to combine the p-values of the max based and sum based tests, which performs well under both dense and sparse alternatives. The combined test relies on the asymptotic independence of the max based and sum based test statistics, which we show rigorously. We show that the proposed max based and combined tests have attractive theoretical properties and demonstrate the superior performance via extensive simulation results. We apply the two new tests to analyze the weekly returns on the securities in the S\&P 500 index under the Fama-French three-factor model, and confirm the usefulness of the proposed combined test in detecting cross-sectional independence.

翻译：检验面板数据模型中的截面独立性在高维面板计量经济分析中具有基础重要性。近年来，计量经济学家开始关注存在序列依赖性时的这一问题。现有用于检验存在序列相关性的截面独立性的方法基于样本截面相关系数之和，该方法在备择假设具有密集截面相关性时表现良好，但在面对稀疏备择假设时功效较低。为应对稀疏备择假设，我们提出了一种基于平方样本截面相关系数最大值的检验方法。此外，我们提出了一种组合检验，将基于最大值与基于总和的检验的p值进行合并，该组合检验在密集和稀疏备择假设下均表现优异。组合检验依赖于基于最大值与基于总和的检验统计量的渐近独立性，我们对此进行了严格证明。我们证明了所提出的基于最大值和组合检验具有优越的理论性质，并通过大量模拟结果展示了其卓越性能。我们将这两个新检验应用于Fama-French三因子模型下标准普尔500指数成分证券的周收益率分析，验证了所提出的组合检验在检测截面独立性方面的实用性。