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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?

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    $\begingroup$ You might consider a hierarchical GLM. Gelman and HIll's "Data Analysis Using Regression and Multilevel/Hierarchical Models" is a good reference on the subject. $\endgroup$ – John Mar 27 '17 at 17:16
  • $\begingroup$ As I understood this was useful when data is coming from different populations and one wished to build a forecast for each/all of said populations. If I am understanding, you are suggesting that each month is a new population. But is there a framework in which one can forecast for new populations; i.e. in my setting to forecast the future? $\endgroup$ – Lepidopterist Mar 27 '17 at 19:08
  • $\begingroup$ Ignore my first comment. I don't think I had read your question carefully enough. Hierarchical GLM won't help you much if you don't have the underlying data. At best, you could assume that the underlying data is missing and put in some assumptions or something, but I'm not sure what it will get you. $\endgroup$ – John Mar 27 '17 at 20:50
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    $\begingroup$ Instead, think about what makes up the average customer investment. There are two drivers: changes in the market, and net contributions/redemptions from accounts. I would probably focus on the log changes in average customer balance, assuming you don't have much information on the underlying contributions or redemptions. This would at least be a function of market variables. It would be lumpy because sometimes large investors might exit. Also, don't forgot new customers. $\endgroup$ – John Mar 27 '17 at 20:51
  • $\begingroup$ @John Are you sure we can give up on the hierarchical GLM? It sounds like an interesting approach if there is any way to justify it. We don't know how an observation at time t-1 relates to an observation at time t, but we do have good information about the average behavior. And we can suppose that there aren't any/many accounts that will grossly distort estimates. The missing link for me is that I'm not able to understand exactly how a HGLM would work if we did have true panel data. $\endgroup$ – Lepidopterist Mar 28 '17 at 0:42

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