Dynamic factor

A dynamic factor is a series which measures the comovement of many time series. It is used in macroeconomic models.

Formally

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

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