This paper studies alpha testing in a high-dimensional conditional time-varying factor model with temporally dependent observations. Both factor loadings and alpha processes are allowed to vary smoothly over time, and the cross-sectional dimension may be comparable to or larger than the sample size. Using a B-spline sieve method, we develop a sum-type test for dense alternatives, a max-type test for sparse alternatives, and a Cauchy combination test for adaptive inference. On the theoretical side, we derive explicit stochastic expansions for the estimated average alphas, establish asymptotic normality of the sum statistic, and develop the extreme-value limit theory for the max statistic by showing its Gumbel convergence under temporal dependence together with the validity of block-bootstrap calibration. We further prove asymptotic independence between the sum and max statistics and thereby justify the Cauchy combination test. Simulation results demonstrate that the proposed procedures achieve satisfactory size control and competitive power across a wide range of dense and sparse alternatives. An empirical application further illustrates the usefulness of the proposed methods in testing asset-pricing models with time-varying structure.

翻译：本文研究在时间相依观测条件下，高维条件时变因子模型中的阿尔法检验问题。允许因子载荷与阿尔法过程随时间平滑变化，且横截面维度可与样本量相当或更大。采用B样条插值法，我们分别针对密集备择假设提出和检验、针对稀疏备择假设提出最大值检验，以及针对自适应推断提出柯西组合检验。理论方面，推导了估计平均阿尔法的显式随机展开式，建立和统计量的渐近正态性，并证明在时间相依条件下最大值统计量的极值极限理论（其服从耿贝尔收敛）及块状自举校准的有效性。进一步证明和统计量与最大值统计量之间的渐近独立性，从而验证柯西组合检验的合理性。模拟结果表明，所提方法在密集与稀疏备择假设下均能实现理想的规模控制与竞争性检验力。实证应用进一步验证了所提方法在检验具有时变结构的资产定价模型中的有效性。