Solved – Time series quantile regression

forecastingquantile regressiontime series

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.

Best Answer

why not use the observed data and generate a forecast and a probability distribution via montecarlo for each period in the future. Review the probability distributions and identify whatever "tile" that you wish.

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