Mode‐adaptive factor models

Factor models are indispensable tools in economics and finance, providing valuable insights into the latent structures underlying complex datasets. Nevertheless, the prevalence of heavy‐tailed macroeconomic and financial data, often characterized by extreme values and greater skewness than that found in a normal distribution, presents significant analytical challenges. This article introduces mode‐adaptive factor models (MAFM) for robust factor analysis in high‐dimensional panel data, inspired by the equivalence between conventional principal component analysis and the constrained least squares method in factor models. Unlike traditional factor models that concentrate on mean estimation, MAFM leverage the mode to capture central tendencies more effectively, particularly in the presence of skewed and heavy‐tailed distributions. To facilitate MAFM for factor analysis, we develop an iterative mode regression algorithm that integrates the expectation‐maximization procedure, ensuring convergence to a stationary solution. We establish the theoretical properties of the MAFM estimators without imposing moment constraints on idiosyncratic errors and propose a mode information criterion for consistent factor number selection. We also suggest a data‐dependent bandwidth selection procedure to enhance the flexibility of MAFM. The simulation studies demonstrate the effectiveness of MAFM across diverse distributional settings. An empirical application to macroeconomic forecasting further highlights the practical advantages of MAFM, showcasing their robustness and efficacy in real‐world analyses.