Example: weather data. You know the location data, but you don't know the previous days'/weeks' temperatures and other weather conditions. How can you exploit these variables in your past data when you build a predictive model that attempts to forecast pretty far out into the future?
How to take advantage of variables whose values are available in the past but not in the future?
predictive modeling
My generic answer to the title is to use the extra data for regularization in representation learning; a transformation of your features into a space conducive to your main task: regression (prediction, forecasting). Here's a survey [PDF].For your example, you could build a model that takes the delay of the target time from the present as an input, so you can predict arbitrarily far into the future, though it probably would not predict as well as a simple regressor that has a fixed horizon since it is trying to learn a more complex function.