STABILITY OF LINEAR MODELS UNDER TEMPORAL AGGREGATION
证明，当收益数据由多元Lévy过程生成时，线性因子模型在降低收益频率时渐近有效，并给出收敛速度条件；同时发现组合的模型误差可能小于个股。
Linear factor models dominate the field of empirical asset pricing and are largely considered a successful framework even though testing for model adequacy is uncommon in empirical research. This article develops a probabilistic argument under the assumption that return data are generated by a multivariate Lévy process and shows that linear factor models are asymptotically adequate as the return frequency declines. Rate-of-convergence results are provided assuming finite or infinite second moments and the moment conditions that determine the convergence rate are analyzed. Separately, we consider the combination of cross-sectional and temporal aggregation, which concerns portfolio applications, and we find that the model error of the linear framework can be smaller for portfolios than individual stocks. Although the intended application is finance, the results in the article are valid in other areas where data aggregation is natural.