Suppose I am supplying $N = 1000$ vendors, and I am looking for a way to predict their demand for my product over $T = 90$ days. Concretely, I hope to take some features for each vendor, such as their size, geographical location etc., as well as their historical demand over some window of $w$ days, and predict their demand on day $w + 1$.
As input data for this problem, I have a dataset on vendor demand over a 90 day window, but the crucial issue is that for any particular vendor, they may arbitrarily report late. For example, if I queried vendor A on day 10 for their demand, they may only report their demand 2 days later, on day 12 (and so I am missing data on day 10 as well as day 11). This behavior varies across vendors, randomly, so that some vendors might report 1 day late; others may report 6 days late.
My question is: Can any predictive model trained on such a data set be meaningful, given this missing data mechanism? Assume that at a population level, I have some amount of demand data for any given window $w$ (but that this is not necessarily true for at the level of particular vendors). Moreover, if I wanted to avoid imputation, as doing this with $N = 1000$ seems to potentially introduce a lot of error, what would be a principled way to preprocess this dataset for the prediction task?