Determining the number of factors in constrained factor models via Bayesian information criterion
提出基于约束贝叶斯信息准则的方法，用于估计约束和部分约束因子模型中的因子数量，通过蒙特卡洛模拟证明其在小样本下表现优于其他方法。
This paper estimates the number of factors in constrained and partially constrained factor models (Tsai and Tsay, 2010 Tsai, H., Tsay, R. (2010). Constrained factor models. Journal of the American Statistical Association 105(492):1593–1605. doi:https://doi.org/10.1198/jasa.2010.tm09123[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) based on constrained Bayesian information criterion (CBIC). Following Bai and Ng (2002 Bai, J., Ng, S. (2002). Determining the number of factors in approximate factor models. Econometrica 70(1):191–221. doi:https://doi.org/10.1111/1468-0262.00273[Crossref], [Web of Science ®] , [Google Scholar]), 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.