Determining the number of factors in constrained factor models via Bayesian information criterion

Abstract

This paper estimates the number of factors in constrained and partially constrained factor models (Tsai and Tsay, 2010) based on constrained Bayesian information criterion (CBIC). Following Bai and Ng (2002), the estimation of the number of factors depends on the tradeoff between good fit and parsimony, so we first derive the convergence rate of constrained factor estimates under the framework of large cross-sections (N) and large time dimensions (T). Furthermore, we demonstrate that the penalty for overfitting can be a function of N alone, so the BIC form, which does not work in the case of (unconstrained) approximate factor models, consistently estimates the number of factors in constrained factor models. We then conduct Monte Carlo simulations to show that our proposed CBIC has good finite sample performance and outperforms competing methods.