In this study, we introduce three distinct testing methods for testing alpha in high dimensional linear factor pricing model that deals with dependent data. The first method is a sum-type test procedure, which exhibits high performance when dealing with dense alternatives. The second method is a max-type test procedure, which is particularly effective for sparse alternatives. For a broader range of alternatives, we suggest a Cauchy combination test procedure. This is predicated on the asymptotic independence of the sum-type and max-type test statistics. Both simulation studies and practical data application demonstrate the effectiveness of our proposed methods when handling dependent observations.

翻译：本研究提出了三种针对高维线性因子定价模型中相依数据Alpha检验的不同方法。第一种方法为和型检验程序，在处理密集备择假设时表现出优异性能。第二种方法为最大值型检验程序，对稀疏备择假设尤为有效。针对更广泛类型的备择假设，我们建议采用柯西组合检验程序，该方法基于和型与最大值型检验统计量的渐近独立性。模拟研究与实际数据应用均证明了所提方法在处理相依观测数据时的有效性。