Dynamic Factor Models and Cointegration

Marco Brianti, Mario Forni, Luca Gambetti and Antonio Granese

No 22037, CEPR Discussion Papers from Centre for Economic Policy Research

Abstract: The factors of a stationary Dynamic Factor Model (DFM) are the first differences of singular I(1) processes. Being singular, such processes are always cointegrated. This however does not prevent the existence of a VAR for their first differences, so that the standard estimation procedure of the stationary DFM remains valid. Problems arise only when there is a linear combination of the shocks that has transitory effects on all the variables of the panel. We argue that this case is implausible for macroeconomic data and show that in fact it does not occur for two widely used US data sets — the FRED-QD and the FRED-MD. A Monte Carlo exercise shows that the standard procedure outperforms alternative methods based on the factors in levels, especially at long horizons.

Keywords: Dynamic factor models; Singular stochastic vector; Cointegration; Common trend; Impulse response functions (search for similar items in EconPapers)
JEL-codes: C32 E32 (search for similar items in EconPapers)
Date: 2026-10
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