Suppose I have a kind of panel data set, where we track the investment totals of a great many customers, which may be highly variable, and is measured on a monthly basis over the course of 7-10 years. While we are ultimately interested in forecasting the total level of investment of all of our customers, for various reasons we find it desirable to factor the analysis into two stages. First, forecast the rate at which old customers close their accounts (and a separate analysis for new customers, which we'll forget about for this question). Second, forecast the average investment of each remaining customer. Unfortunately, this is not a true panel data set and we are unable to track one customer across time. Strange, I know!
We hypothesize that length-of-customer-relationship and one or two specific macroeconomic variables might drive the two processes.
The current approach is to model customer attrition with a logistic regression model, and to model average customer investment with a gamma GLM. This seems reasonable to me, having previous experience with only non-economic data. However, I have a concern. As this data is a pseudo panel data set, with large N but small time T, it's not clear that regression assumptions are satisfied. There is surely some correlation within accounts for a given month/year. And furthermore, though I only understand it vaguely, there are issues when some of our macroeconomic predictors are stochastic and non-stationary.
Can we use these GLM models for this data set? If we had a true panel data at least know the literature to read, but in this case my intuition tells me that a GLM should work, although we have to be careful about interpreting the standard errors, etc.
Should I radically reconsider the GLM models or is there a way to justify it in this context? Is there some specific literature that I might be advised to look into?