Common Factors and Common Shocks: A Tale of Three (Close) Signal Extraction Procedures

Three main specifications of dynamic factor models (DFMs) are popular to represent the commonality often present in large systems of time series. First, traditional DFMs assume that the commonality in the series depends on common contemporaneous underlying factors, which may have temporal dependences. Second, finite-dimensional generalized DFMs (FDG-DFMs) consider common factors loaded through finite lag structures. Third, the G-DFM defines the common components in terms of contemporaneous and lagged underlying common white noise shocks, allowing for infinite lag structures. Different signal extraction procedures have been proposed for each of the three specifications. In this chapter, we compare them in the context of estimation of common components, when one of them can be identified with a factor, which can be interpreted as an underlying economic index.