Fast forecast reconciliation using linear models

Mahsa Ashouri, Rob J. Hyndman, Galit Shmueli

Research output: Contribution to journalArticleResearchpeer-review

4 Citations (Scopus)


Forecasting hierarchical or grouped time series using a reconciliation approach involves two steps: computing base forecasts and reconciling the forecasts. Base forecasts can be computed by popular time series forecasting methods such as exponential smoothing (ETS) and Autoregressive Integrated Moving Average (ARIMA) models. The reconciliation step is a linear process that adjusts the base forecasts to ensure they are coherent. However, using ETS or ARIMA for base forecasts can be computationally challenging when there are a large number of series to forecast, as each model must be numerically optimized for each series. We propose a linear model that avoids this computational problem and handles the forecasting and reconciliation in a single step. The proposed method is very flexible in incorporating external data. We illustrate our approach using a dataset on monthly Australian domestic tourism, as well as a simulated dataset. We compare our approach to reconciliation using ETS and ARIMA, and show that our approach is much faster while providing similar levels of forecast accuracy. Supplementary files for this article are available online.

Original languageEnglish
Pages (from-to)263-282
Number of pages20
JournalJournal of Computational and Graphical Statistics
Issue number1
Publication statusPublished - 2022


  • Grouped forecasting
  • Hierarchical forecasting
  • Linear regression
  • Reconciling forecast

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