I am regressing gross sales against two regressors X1 and X2, and have a linear regression model with me. I want to use this model to get forecasts far out into the future where the values of X1 and X2 are not available. Can I even meaningfully use this model to make such forecasts? How will I get the values of X1 and X2? I understand that in a regular setting we split the data into a training and a test set, build the model using the training set, and test it using the test set. But we do have the values of the predictors/regressors in the test set while testing the model. But while using the model to make forecasts far out into the future we might not have the values of the predictors. Can the model be used in such a situation? If yes, how?
Without values for X1 and X2 (the predictors), you cannot compute predicted values for gross sales using the linear model.
As far as the training/test set, this procedure is used more for assessing model fit and predictive power and will not help you in this situation. You still need known values for your predictors.
If you have the means to estimate your predictors in the future, you can then use them in the model to make predicted values of gross sales.
Take a look at https://autobox.com/pdfs/regvsbox-old.pdf to get some idea about how to do regression with time series data . Ordinary regression procedures requires independent ( i.e. non-time series ) data.
In terms of predicting the predictors use arima and MAKE SURE THAT THE UNCERTAINTY IN THE PREDICTORS IS incorporated into the uncertainty of Y .