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.
Stoyan Stoyanov (Wed,) studied this question.