Constant term in time series econometric models built on 1-st differences Both dependent and independent variables I deal with are nonstationary series that become stationary after differentiating them once.
The problem is that I assume that the dependent variable has a certain constant value which does not depend on the explanatory variables' changes and should be estimated as the model's constant term. 
But the constant term is lost in the process of differentiation. 
Does anyone know any method of dealing with that kind of problem?
 A: As @IrishStat said it depends on the model. One way of recovering constant is to use the mean value of the residuals. Note that this method relies strongly on certain assumptions. Here is the illustration. Suppose your model is
$$Y_t=\alpha + \beta X_t + \varepsilon_t$$
with
$$E(\varepsilon_t|X_t)=0$$
and you estimate it by
$$\Delta Y_t=\beta \Delta X_t+\Delta \varepsilon_t.$$
Suppose your estimate $\hat\beta$ is unbiased (or at least consistent). Define
$$\hat{e}_t=Y_t-\hat\beta X_t.$$
Substituting the true model we have
$$\hat{e}_t=\alpha+\varepsilon_t+(\beta-\hat\beta)X_t,$$
hence
$$E(\hat{e}_t|X_t)=\alpha,$$
if $\hat\beta$ is unbiased or  
$$\frac{1}{T}\sum_{t=1}^T\hat{e}_t\to \alpha,$$
if $\hat\beta$ is consistent.
So the natural estimate for $\alpha$ is
$$\hat{\alpha}=\frac{1}{T}\sum_{t=1}^T(Y_t-\hat\beta X_t).$$
Note that the model assumption is critical here. However with care this trick can be applied in general.
A: All software I know allows the user to specify whether or not a constant is included in the model. What software are you using ? Do you wish to share data (coded or not) and the model you are trying to estimate and perhaps I caN shed some light on "stuff"
ADDITIONAL MATERIAL ADDED !
When Y and X can be rendered stationary by suitable differencing , we do so to IDENTIFY the relationship between Y and X. Just because Y and X need to be differenced for IDENTIFICATION PURPOSES does not mean the differencing needs to be incorporated into the Transfer Function (econometric model) . For example both Y and X may be non-stationary BUT  the relationship between Y and X may be as simple as  Y(t)=B0 + b1*X(T) +A(t) . If one was naive enough to difference both Y and X then one would be inducing an ARIMA component into the model viz.   [1-B]Y(t)=[1-B]X(t)+ [1-theta*B]*A(t) where the estimated theta1 would be aprroximately equal to 1.0. Some programs ( you can guess the usual suspects) actually ASSUME that differencing required for IDENTIFICATION is the same as differencing in the final ESTIMATED MODEL. Hope my commentary helps you !
