Time-Varying Structural Approximate Dynamic Factor Model

This study proposes a time-varying structural approximate dynamic factor (TVS-ADF) model by extending the ADF model in state-space form. The TVS-ADF model considers time-varying coefficients and a time-varying variance–covariance matrix of its innovation terms, so that it can capture complex dynamic economic characteris- tics. We propose the identification scheme of the common factors in the TVS-ADF and derive the identification theory. We also propose an effective Markov chain Monte Carlo (MCMC) algorithm to estimate the TVS-ADF. To avoid the overparameterization caused by the time-varying characteristics of the TVS-ADF, we include the shrinkage and sparsification approaches in the MCMC algorithm. Additionally, we propose several effective information criteria for the determination of the number of factors in the TVS-ADF. Extensive artificial simulations demonstrate that the TVS-ADF has better forecast performance than the ADF in almost all settings for different numbers of explained variables, numbers of explanatory variables, sparsity levels, and sample sizes. An empirical application to macroeconomic forecasting also indicates that our model can substantially improve predictive accuracy and capture the dynamic features of an economic system better than the ADF.