Time Series regresison - issues with Stationarity/Residuals


New Member
We set up an OLS model about 6 months ago, using time series data (both the dependent and independent variables are Monthly data). The model has 2 independent continuous time series and 2 other (categorical and numeric) variables. Initially, we did not think it necessary to specifically conduct stationarity tests, and only performed Log or Differencing transformations on the independent variables, believing that this would be sufficient for our purpose. However, now we are taking another look. I find that the Differenced predictor is Stationary ( Unemployment Rate) but the other predictor which was logged (Consumer price Index) is not Stationary (when plotted, the Log of CPI shows a small positive slope).
However, the residuals of the model as a whole are stationary, and the residuals obtained from regressing just Log of CPI against the dependent are also stationary.
We are also only interested in forecasts in the next say, 6 quarters (where the values of the predictors don't change much - based on internal projections for these predictors). Under these circumstances, is our Model okay to use (of course subject to revision within the next 5 or 6 quarters)- the main point in our favour being that the residuals are stationary?
Note that the time series of the dependent variable is trend-stationary but we don't (and based on our constraints, can't) have a Time variable T in the model to catch the trend. Thanks for your advice!