Forward stepwise regression procedure: application to panel data

I am in the process of evaluating the importance of some factors in predicting stock returns. In this context, I would like to implement the forward stepwise regression methodology. My dataset is comprised of 13,000 securities with monthly data from 1984 to 2012.

Since this is my first application of the methodology using panel data, I am not sure of the right way to proceed in order to determine the final set of predictors to be included in the model.

According to the methodology, all the predictors will be tested, and included (or not) in the factor model based on their p-value.

My question is this: The stepwise regression will be performed using cross-sectional data at time t = 1, and the "right" predictors will be determined using the elimination process. In the context of panel data, would this procedure be replicated for each time t ? If so, we might end up with 348 models (1 for each month from 1984 to 2012). How would we then decide which factors to include in a final model? Would that be based on each factor's frequency of appearance in the monthly models?