Correcting autocorrelation with MA in a regression I would need some advice on a multivariate regression problem. I am running regressions with macroeconomic data at first difference and using a AR(1) as regressor to correct autocorrelation (it makes Eviews do iterative regressions). However some models still contain autocorrelation with this method. 
I tried to introduce a moving average MA(1) in the model and the regression didn’t show any more autocorrelation. But am I allowed to use a MA(1) as a regressor ? For example can I estimate X = c + a*Y + MA(1) + AR(1) ?
If not, would you have another method to eliminate autocorrelation?
 A: What you are referring to are ARIMA models.They consist of AR, MA and Integrated component(first difference). You can read about them in detail.
You're allowed to use anything as long as you don't use future data in you model.
P.S. If this doesn't answer your question, please guide me about what your query is about.
A: If you have regressions of the form
$$ y_t = \beta_0 + \beta_1 x_{1,t} + \dotsc + \beta_K x_{K,t} + \varepsilon_t $$
where the $x$s are exogenous and you are interested in $\beta$s* (which could be thought of as structural parameters), then you may try regression with ARMA errors (see e.g. here). This setup preserves the original model (so you obtain $\beta$s immediately) and at the same time fixes the problem of autocorrelated errors. You could implement the model in R by using functions arima or auto.arima supplying them with exogenous regressors (the $x$s).
It would be something similar (although not quite the same) as your idea of including both AR and MA terms directly into the model equation. That would result in an ARMAX model (see the same source), which is a valid model, although its coefficients may be a little difficult to interpret.
If, on the other hand, you have regressions of the form
$$ y_{1,t} = \beta_0 + \beta_1 x_{1,t} + \dotsc + \beta_K x_{K,t} + \gamma_2 y_{2,t} + \dotsc + \gamma_L y_{L,t} + \varepsilon_t $$
(with or without $x$s) where $y$s are endogenous, you have a problem which cannot be solved by running a regression with ARMA errors nor an ARMAX model. Some (or all) of the regressors being endogenous is against the model assumptions and ruins the nice properties of coefficient estimators, so you cannot trust the coefficient estimates nor their standard errors. In such a setting, (structural) vector autoregressions ((S)VARs) are used. If you are not interested in $\gamma$s, you may build a VAR model and look into its impulse response functions (IRFs) and forecast error variance decomposition (FEVD) to see how the different variables interact. However, if you are interested in $\gamma$s, you would need a SVAR model, which is a little more involved. 
* For example, you want to test some hypotheses based directly on $\beta$s. 
