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I'm conceptualizing a methodology for a time series forecast but I lack the terminology and even the notation to learn more or even adequately describe it.

Suppose I aim to forecast the aggregate response to an ad campaign (both the mean likelihood $\hat y_t$ and the probability distribution) at future time $t$.

I'd like to develop a model not only using aggregate-level data from past campaigns, but individual customer-level samples. For instance, I may have instances of individual customers included in past campaigns, along with demographic and economic indicators for the individual customer along with the date the customer responded to the campaign.

Using this dataset, I could estimate the probability of an individual customer responding at $t_0$ (start of campaign), $t_1$ (day 1), $t_2$, ...., and creating new probability estimates each day based on the previous day's responses (akin to a survival analysis).

I'd like to apply this model to a new set of customers for a future campaign to estimate not only an individual's likelihood to respond by a given day based on individual-level predictors (age, income, etc.), but also using time-series methods as the campaign progresses (e.g. how many similar customers responded the previous day?).

It seems like this could be done with something like a Markov chain Monte Carlo by creating an individual-level prediction at $t_0$, sampling from the distribution, and using both known unit-level inputs as well as simulated outcomes from the previous day. As the campaign progresses, the inputs could be updated and new individual-level probabilities created and simulated for the future.

I apologize for the lack of precision in terminology, but again, that's exactly what I'm lacking to better research the concept. What would this approach and these concepts be called?

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  • $\begingroup$ See otexts.com/fpp2/hierarchical.html for some related ideas. $\endgroup$
    – Rob Hyndman
    Commented May 5, 2020 at 1:29
  • $\begingroup$ Thank you @RobHyndman, this is very helpful. I hadn't thought about it this way, but my problem is similar to a hierarchical time series where my "bottom" group is actually a binary outcome. I suppose it would be similar to the Australian prison population example in section 10.2, except my bottom-level group would be a data set of every Australian resident with a binary outcome indicating whether or not they were imprisoned on a given day. $\endgroup$
    – danpelota
    Commented May 5, 2020 at 19:30

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