# Optimal forecast reconciliation for hierarchical and grouped time series through trace minimization

Large collections of time series often have aggregation constraints due to product or geographical groupings. The forecasts for the most disaggregated series are usually required to add-up exactly to the forecasts of the aggregated series, a constraint we refer to as “coherence”. Forecast reconciliation is the process of adjusting forecasts to make them coherent. The reconciliation algorithm proposed by Hyndman et al. (2011) is based on a generalized least squares estimator that requires an estimate of the covariance matrix of the coherency errors (i.<img src=“http://feeds.feedburn …