Multicollinearity and time series.

[NIP NIP]

Hello!

Please, share you experience on the following. And correct me if I'm wrong.

Multicollinearity is an issue of the data, not of any model. Let's say we want to estimate a regression model via OLS, using time-series. Think of an ARDL model. If lagged variables introduce multicollinearity, why time-series analyst do not seem to be bother (I think) by multicollinearity.

[Andrew Musau]

You do not see distributed lag models (i.e., models that explain current values of \(Y\) as a function of past and current values of \(X\)) being estimated using OLS. One of the reasons is exactly the various lagged values of \(X\) are likely to be severely multicollinear, making coefficient estimates imprecise. Because of this multicollinearity, there is no guarantee that the estimated coefficients will follow the pattern predicted by theory. For example, economic theory predicts that expansions or contractions in money supply far in the past will have a lesser effect on current GDP relative to expansions or contractions in the recent past (i.e, there is a declining pattern). For such economic variables, you apply the Koyck transformation to turn the distributed lag model into a dynamic model (a model with a lagged dependent variable). Then you estimate this model - other problems like serial correlation arise, but there is no multicollinearity. You may find the following useful reading: https://www.jstor.org/stable/1907516