We propose a simple estimator for the dynamic decomposition of the Generalized Dynamic Factor Model that avoids frequency-domain methods. First, we show that it is a reasonable approximation to assume that the dynamic common component of the Generalized Dynamic Factor Model admits a representation in terms of current and lagged statically pervasive factors. Then, assuming finite lag order, this simplification reduces estimation to a regression of the observed variables on estimated factors and their lags, where the factors are extracted via static principal components. The proposed approach naturally accommodates weak, non-pervasive factors within the dynamic common space. We establish consistency and asymptotic normality for both the dynamic and weak common components under a new asymptotic framework that allows for such weak factors. In an application to three high-dimensional time series panels of European macroeconomic data we detect a sizeable weak common component share in several key macroeconomic indicators.

翻译：针对广义动态因子模型的动态分解问题，我们提出一种避免频域方法的简易估计方案。首先证明，假设广义动态因子模型的动态共同成分可用当前及滞后静态渗透因子的表示形式进行合理近似。在此基础上，若滞后阶数有限，则可将估计问题简化为将观测变量对估计因子及其滞后项进行回归，其中因子通过静态主成分分析法提取。该方法可自然容纳动态共同空间中的弱非渗透因子。通过建立允许弱因子存在的新渐近框架，我们证明了动态共同成分与弱共同成分的一致性与渐近正态性。在对三组欧洲宏观经济数据高维时间序列面板的实证应用中，多个关键宏观经济指标均检测到显著的弱共同成分占比。