Optimal Forecast Reconciliation for Hierarchical and Grouped Time Series Through Trace Minimization

By Shanika L. Wickramasuriya, George Athanasopoulos, Rob J Hyndman. 2018

345 citations recorded by the source corpus.

ABSTRACT 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.e., the errors that arise due to incoherence). We show that this matrix is impossible to estimate in practice due to identifiability conditions. We propose a new forecast reconciliation approach that incorporates the information from a full covariance matrix of forecast errors in obtaining a set of coherent forecasts. Our approach minimizes the mean squared error of the coherent forecasts across the entire collection of time series under the assumption of unbiasedness. The minimization problem has a closed-form solution. We make this solution scalable by providing a computationally efficient representation. We evaluate the performance of the proposed method compared to alternative methods using a series of simulation designs which take into account various features of the collected time series. This is followed by an empirical application using Australian domestic tourism data. The results indicate that the proposed method works well with artificial and real data. Supplementary materials for this article are available online.

Subfields: Management Science and Operations Research, Signal Processing

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In Management Science and Operations Research

1. Rafal Weron
2. Tao Hong
3. Yanfei Kang
4. Feng Li
5. Xiaoqian Wang
6. Dazhi Yang
7. Pierre Pinson
8. H. Zareipour

In Signal Processing

1. Yanfei Kang
2. Feng Li
3. Xiaoqian Wang
4. Rob J Hyndman
5. Rajat Sen
6. Weihao Kong
7. Yichen Zhou
8. Abhimanyu Das

Citations in the corpus

• Forecast combinations: An over 50-year review (2022, methodology): “, Winkler (1968), Clemen and Winkler (1993), Clemen and Winkler (1985), and Jouini and Clemen (1996).”
• Energy Forecasting: A Review and Outlook (2020, background): “Over several publications, computation issues that hinder the large-scale applications of hierarchical forecasting have been addressed [46]–[48].”
• A decoder-only foundation model for time-series forecasting (2023, methodology): “Subsequently, we perform ablation studies that justify different choices made in our architecture.”