This paper focuses on testing for the presence of alpha in time-varying factor pricing models, specifically when the number of securities N is larger than the time dimension of the return series T. We introduce a maximum-type test that performs well in scenarios where the alternative hypothesis is sparse. We establish the limit null distribution of the proposed maximum-type test statistic and demonstrate its asymptotic independence from the sum-type test statistics proposed by Ma et al.(2020).Additionally, we propose an adaptive test by combining the maximum-type test and sum-type test, and we show its advantages under various alternative hypotheses through simulation studies and two real data applications.

翻译：本文聚焦于时变因子定价模型中Alpha存在性的检验问题，特别关注证券数量N大于收益率序列时间维度T的情形。我们提出一种最大值型检验统计量，该检验在备择假设稀疏的场景下表现优异。我们建立了所提出的最大值型检验统计量的极限零分布，并证明其与Ma等人(2020)提出的总和型检验统计量渐近独立。此外，我们通过结合最大值型检验与总和型检验构建自适应检验方法，并通过模拟研究与两项真实数据应用展示了该方法在不同备择假设下的优势。