problems with autocorrelated residuals

[borto91]

Hi all econometricians!

I'm developing a little project for my Econometrics exam at the University. I have downloaded some time series (monthly and seasonal adjusted) from online St. Louis FED database. I have checked if it was better to transform the data (log), I have checked for the presence of unit roots (they are all I(1)). I have estimated at least three (static) models (all with different variables) and every model I'm trying to estimate give me autocorrelated and heteroskedastic residuals. The problem is that I don't know how to set up the model: someone tells me that in a static model, all variables have to be at time t (no lags) don't worrying about the order of integration; some other tells me that I should have variables I(1) in order to take advantage of cointegration and superconsistency of the estimates (so, if one is I(2), i have to put it lagged in the equation); again, some other tells me that the variables have to be all I(0) (so putting also lags in the equation, if needed). By the way, everyone of this ways give me autocorrelated and heteroskedastic residuals; the only case in which I'm uncorrelated and homoskedastic is when I put all my variables lagged by 1 in the equation, but I think this produces a poor of significance relation. I don't know what is my problem and the best way to operate. :( So I'm here to ask your help.
Thank you in advance.

(eViews 7)

update: it seems that in my last model, if a put only the dependent variable in first difference (so, it becomes stationary and all the independent variables are non-stationary), the problem seems to be solved: no autocorrelation and no heteroskedasticity; but why should I decide to lag the dependent variable?

[borto91]

I decided to try to over-differenciate my dependent variable and, magically, no more spurious regressions! I'm no more autocorrelated nor heteroskedastic. it seems that, in general, there are not so much problems in over-difference: what do you think about?