Factors in Fashion: Factor Analysis towards the Mode

TL;DR

This paper introduces a novel modal factor model for dimension reduction in high-dimensional panel data, focusing on the conditional mode rather than the mean, with proven asymptotic properties and practical inflation forecasting applications.

Contribution

It develops a new modal factor model with an efficient estimation algorithm, model selection criteria, and demonstrates its advantages over traditional mean-based models.

Findings

Estimators perform well in finite samples, even with heavy-tailed errors.

The modal factor model outperforms mean-based models in inflation forecasting.

Asymptotic properties of estimators are rigorously established.

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.