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I have time series data and want to perform multiple regression. I have three time series independent variables that i want to include in the regression model. Before doing any analysis do I need to remove the trend from all data sets ( dependent and independent variables)?

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Yes, you do need to detrend all your variables (both X and Y); otherwise you are going to have a mispecified model and a classic example of a "spurious" regression. Clive Granger defined spurious regressions as regressions that often have a very high R Square (close to 1.00) but are absent any economic meaning. Spurious regressions also have typically very highly correlated residuals (Durbin Watson often < 1.2). The reason such regressions have no meaning is that many time series just grow over time. So, your model typically has no more explanatory power than a simple trend variable that counts 1, 2, 3, ...

Some people may argue that you do not need to detrend your variables if the residuals of such regressions are stationary and not too correlated. In such a case, you would have a successful Cointegration model (Clive Granger also published papers on this subject).

However, one may express some reservations on such Cointegration models using variables that are not detrended at all. Such model structure is probably not the best one to extract reliable information on the variables you have tested.

Thus, detrending all your variables (and preferably using the same or similar basis of detrending) is a good foundation to develop a well specified model.

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  • $\begingroup$ Would you agree that you should either de-trend all variables ($X$ and $Y$) or none, but never one but not the other (de-trend $Y$ but not $X$)? $\endgroup$
    – LBogaardt
    Commented Aug 12, 2019 at 13:38
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    $\begingroup$ As you know, I am not in favor of detrending none. Yet, it can result in an acceptable Cointegration model structure. Of course, you have to insure that such variables are cointegrated... which is rarely the case. However, there is one model structure where you can have a de-trended Y variable with a mix of de-trended and level independent variables... and that is in Error Correction Models (ECM). $\endgroup$
    – Sympa
    Commented Aug 14, 2019 at 4:28

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