Pooling information and forecasting with dynamic factor analysis

In this paper, we present a generalized dynamic factor model for a vector of time series, which seems to provide a general framework to incorporate all the common information included in a collection of variables. The common dynamic structure is explained through a set of common factors, which may be stationary, or nonstationary as in the case of common trends. Also, it may exist a specific structure for each variable. Identification of the non stationary factors is made through the common eigenstructure of the lagged co variance matrices. Estimation of the model is carried out in state space form with the EM algorithm, where the Kalman filter is used to estimate the factors or not observable variables. It is shown that this approach implies, as particular cases, many pooled forecasting procedures suggested in the literature. In particular, it offers an explanation to the empirical fact that the forecasting performance of a time series vector is improved when the overall mean is incorporated into the forecast equation for each component.