Dynamic factor

In econometrics a dynamic factor (also known as a diffusion index) is a series which measures the co-movement of many time series. It is used in certain macroeconomic models.

Formally

$X_{t}=\Lambda _{t}F_{t}+e_{t},$

where $F_{t}=(f_{t}^{\top },\dots ,f_{t-q}^{\top })$ is the vector of lagged factors of the variables in the $T\times N$ matrix $X_{t}$ (T is the number of observations and N is the number of variables),$\Lambda _{t}$ are the factor loadings, and $e_{t}$ is the factor error.

Literature

• Forni, Mario & Lippi, Marco, 2001. The Generalized Dynamic Factor Model: Representation Theory, Econometric Theory, vol. 17(6), pages 1113-41.
• Stock, James H & Watson, Mark W, 2002. Macroeconomic Forecasting Using Diffusion Indexes, Journal of Business & Economic Statistics, vol. 20(2), pages 147-62.