Dynamic factor
（重定向自Diffusion index）
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
where ![F_{t}=(f^{\top}_{t},\dots,f^{\top}_{t-q})](/Images/godic/202501/09/01347029fad919e3f0368d337d8d5b1c0052.png")
is the vector of lagged factors of the variables in the ![T \times N](/Images/godic/202501/09/8079dc927fd792920758a9ebdbcf42560052.png")
matrix ![X_{t}](/Images/godic/202501/09/04b2b7370fed516962642f0b34c55b370052.png")
(T is the number of observations and N is the number of variables), ![\Lambda_{t}](/Images/godic/202501/09/f6211be10fffa63b6d58f59b84f447380053.png")
are the factor loadings, and ![e_{t}](/Images/godic/202501/09/e7d3a0e6c9fed6d261a918f545d3a7380053.png")
is the factor error.