The research question we answer in this paper is whether the asymptotic distribution derived by Bai (2003) for Principal Components (PC) factors in dynamic factor models (DFMs) can approximate the empirical distribution of the sequential Least Squares (SLS) estimator of global and group-specific factors in multi-level dynamic factor models (ML-DFMs). Monte Carlo experiments confirm that under general forms of the idiosyncratic covariance matrix, the finite-sample distribution of SLS global and group-specific factors can be well approximated using the asymptotic distribution of PC factors. We also analyse the performance of alternative estimators of the asymptotic mean squared error (MSE) of the SLS factors and show that the MSE estimator that allows for idiosyncratic cross-sectional correlation and accounts for estimation uncertainty of factor loadings is best.

翻译：本文研究并解答的问题是：Bai (2003) 针对动态因子模型 (DFM) 中主成分 (PC) 因子推导的渐近分布，能否有效近似多层级动态因子模型 (ML-DFM) 中全局因子与组别特定因子的序贯最小二乘 (SLS) 估计量的经验分布。蒙特卡洛实验证实，在异质性协方差矩阵的一般形式下，SLS 全局因子与组别特定因子的有限样本分布能够通过 PC 因子的渐近分布得到良好近似。我们还分析了 SLS 因子渐近均方误差 (MSE) 的多种估计量的表现，结果表明：允许异质性截面相关性并考虑因子载荷估计不确定性的 MSE 估计量具有最优性能。