I'm using supervised learning on monthly activity data to predict when a customer buys a particular product. This product is typically bought infrequently and at the moment my target variable is whether the customer buys the product in the next twelve months.
Assume that for every customer I get a set of features every month, $x_1,x_2,\ldots,x_n$. The goal is to use these features to predict whether $y=0$ or $y=1$ ($y$ is 1 if the customer did buy the product in the next twelve months, otherwise it is zero).
However, this creates a dilemma. If I use this approach for $y$ then my freshest training data is twelve months old as I do not know the true value for $y$ for data that is younger than twelve months old. My main question is thus the following: Is there a way for me to make use of newer data in this setting?
Also, I should note that I have tried changing $y$ into: "Does the customer buy the product in the next month?". It works but not nearly as well as the other approach. My data is imbalanced so by allowing the target period to be composed of the following twelve months instead of a single month I get many more positive data points.