Is stationarity assumption needed for a switching model?

[anozman]

The set of explanatory variables are highly correlated with the correlation coefficients around about 0.6 to 0.7.

Regards,
Anozman

[TomDoan]

That's not even very high.

"Multicollinearity" was a serious problem about 40 years ago when most statistical software worked in single precision. It faded as an issue with double precision floating point calculations and improved inversion/factoring algorithms. Newer textbooks generally don't even mention "near" collinearity---only exact collinearity (such as the dummy variable trap). Big sections on multicollinearity usually only exist in textbooks which were originally written in the 1970's and 1980's.

[anozman]

Thank you very much Tom. Is multicollinearity still a problem for normal linear time series models?

Regards,
Anozman

[TomDoan]

Thank you very much Tom. Is multicollinearity still a problem for normal linear time series models?

Regards,
Anozman

The textbook description of multicollinearity is always applied to linear models. Again, it's an issue only if you happen to be using software that hasn't been updated since maybe 1985.

[anozman]

Hi Tom,

My understanding is that multicollinearity is not just about whether the parameters can be estimated reliably, it may cause the good variables to be "wrongly" excluded from the final equation. This is my main concern especially when I do not know with priori knowledge and a theory to guide variable selection.

Regards,
Anozman

[TomDoan]

I have no idea what result it is that you're trying to cite as the basis for that "understanding". If X1 and X2 are highly correlated, you can't tell whether X3 should be in the model? That's a new one on me. If X1 and X2 are highly correlated, you can't tell which should be in the model? OK. That's true. And that's the world of non-experimental statistics---it's hard to tell which of several possible measures (proxies) for an unobservable quantity is best. None are perfect. And...there's nothing you can really do about it. X1 and X2 are what they are.