The paper presents a generalized dynamic factor model (GDFM) that allows for non-orthogonal idiosyncratic components, extending previous static and exact factor models. The model is identified under certain conditions, and an estimator is proposed that converges to the common factor as the time and cross-sectional dimensions grow. Simulations show good performance in small samples, and an empirical example on US state output growth illustrates the method. The model is dynamic, allows for infinite cross-sectional dimensions, and accommodates both autoregressive and moving average factors. Key assumptions include bounded spectral densities and diverging common eigenvalues. The paper shows that the common component can be recovered asymptotically using dynamic principal components, and provides an estimator based on these components. The model is compared to static factor models, and the choice of the number of factors is determined by analyzing eigenvalues. The paper also discusses the estimation of the common component using OLS regressions on dynamic principal components, and presents simulation results showing the effectiveness of the method. The empirical example demonstrates the application of the model to real data.The paper presents a generalized dynamic factor model (GDFM) that allows for non-orthogonal idiosyncratic components, extending previous static and exact factor models. The model is identified under certain conditions, and an estimator is proposed that converges to the common factor as the time and cross-sectional dimensions grow. Simulations show good performance in small samples, and an empirical example on US state output growth illustrates the method. The model is dynamic, allows for infinite cross-sectional dimensions, and accommodates both autoregressive and moving average factors. Key assumptions include bounded spectral densities and diverging common eigenvalues. The paper shows that the common component can be recovered asymptotically using dynamic principal components, and provides an estimator based on these components. The model is compared to static factor models, and the choice of the number of factors is determined by analyzing eigenvalues. The paper also discusses the estimation of the common component using OLS regressions on dynamic principal components, and presents simulation results showing the effectiveness of the method. The empirical example demonstrates the application of the model to real data.