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 macroeconomic models.

Formally


 * $$ X_{t}=\Lambda_{t}F_{t}+e_{t},$$

where $$F_{t}=(f^{\top}_{t},\dots,f^{\top}_{t-q})$$ 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.