I have time series where at each time step I have a bunch of real-valued points (e.g. individual purchases on a given day), and would like to produce a forecast of several quantiles.
One approach I'm thinking of is, for each quantile, compute the time-series of its empirical values, and forecast those. So if I want 10 quantile predictions, I would produce/forecast 10 separate time-series.
My only concern is that the above approach might yield quantiles that are not ordered. For example, 80th quantile might have a much larger trend than the 90th quantile, and the forecast of the former might be larger than the forecast of the latter.