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Factor Model Lag

Hi,

I've been going through the Fundamental Factor Model lecture and other references; however, something I have not see and I assume it is supposed to be done this way, which is the dependent variable Y inn the linear regression or the independent Variable of the Linear regression should be lagged. Is this correct?

In other words

Yi=α+β1X1i-1+…+βkXki-1+ϵi-1

or

Yi+1=α+β1X1i+…+βkXki+ϵi

This is for prediction. Please confirm