Factor extraction using Kalman filter and smoothing: This is not just another survey

Abstract

Dynamic Factor Models, which assume the existence of a small number of unobserved latent factors that capture the comovements in a system of variables, are the main big data tool used by empirical macroeconomists during the last 30 years. One important tool to extract the factors is based on Kalman lter and smoothing procedures that can cope with missing data, mixed frequency data, time-varying parameters, non-linearities, non-stationarity and many other characteristics often observed in real systems of economic variables. This paper surveys the literature on latent common factors extracted using Kalman lter and smoothing procedures in the context of Dynamic Factor Models. Signal extraction and parameter estimation issues are separately analyzed. Identication issues are also tackled in both stationary and non-stationary models. Finally, empirical applications are surveyed in both cases.

High-dimensional dynamic factor models: a selective survey and lines of future research

“…The paper employs a maximum likelihood estimator for the DFM resulting from the assumption that the idiosyncratic components are cross-sectionally uncorrelated, and shows that this misspecification has no effect on the estimated common components as N → ∞. See also Bai and Li (2016), Barigozzi and Luciani (2019) and Poncela et al (2021). This motivates the following formulation of a DFM in state space.…”

Estimation of Impulse-Response Functions with Dynamic Factor Models: A New Parametrization

“…Interestingly, they also show that when the dynamic factor dimension q is smaller than the static factor dimension r, the EM algorithm performs better than the principal component estimation scheme. Poncela et al (2021) survey comprehensively the literature on the estimation of DFMs using state space models and the EM algorithm.…”

Ignoring Cross-Correlated Idiosyncratic Components When Extracting Factors in Dynamic Factor Models1

“…Alternatively, one can use Kalman Filter and Smoothing (KFS) to extract the factors; see Poncela, Ruiz and Miranda (2021) for a survey. To be ecient, KFS procedures require full specication of the common and idiosyncratic components, which, when the cross-sectional dimension is large, depends on a large number of parameters.…”