Factors in Fashion: Factor Analysis towards the Mode

Abstract: The modal factor model represents a new factor model for dimension reduction in high dimensional panel data. Unlike the approximate factor model that targets for the mean factors, it captures factors that influence the conditional mode of the distribution of the observables. Statistical inference is developed with the aid of mode estimation, where the modal factors and the loadings are estimated through maximizing a kernel-type objective function. An easy-to-implement alternating maximization algorithm is designed to obtain the estimators numerically. Two model selection criteria are further proposed to determine the number of factors. The asymptotic properties of the proposed estimators are established under some regularity conditions. Simulations demonstrate the nice finite sample performance of our proposed estimators, even in the presence of heavy-tailed and asymmetric idiosyncratic error distributions. Finally, the application to inflation forecasting illustrates the practical merits of modal factors.