Probabilistic Reconciliation of Count Time Series

We propose a principled method for the reconciliation of any probabilistic base forecasts. We show how probabilistic reconciliation can be obtained by merging, via Bayes' rule, the information contained in the base forecast for the bottom and the upper time series. We illustrate our method on a toy hierarchy, showing how our framework allows the probabilistic reconciliation of any base forecast. We perform experiment in the reconciliation of temporal hierarchies of count time series, obtaining major improvements compared to probabilistic reconciliation based on the Gaussian or the truncated Gaussian distribution.