Forecasting with Temporal Hierarchies

This paper introduces the concept of Temporal Hierarchies for time series forecasting. A temporal hierarchy can be constructed for any time series by means of non-overlapping temporal aggregation. Predictions constructed at all aggregation levels are combined with the proposed framework to result in temporally reconciled, accurate and robust forecasts. The implied combination mitigates modelling uncertainty, while the reconciled nature of the forecasts results in a unified prediction that supports aligned decisions at different planning horizons: from short-term operational up to long-term strategic planning. The proposed methodology is independent of forecasting models. It can embed high level managerial forecasts that incorporate complex and unstructured information with lower level statistical forecasts. Our results show that forecasting with temporal hierarchies increases accuracy over conventional forecasting, particularly under increased modelling uncertainty. We discuss organisational implications of the temporally reconciled forecasts using a case study of Accident & Emergency departments

Forecasting with Temporal Hierarchies

This paper introduces the concept of Temporal Hierarchies for time series forecasting. A temporal hierarchy can be constructed for any time series by means of non-overlapping temporal aggregation. Predictions constructed at all aggregation levels are combined with the proposed framework to result in temporally reconciled, accurate and robust forecasts. The implied combination mitigates modelling uncertainty, while the reconciled nature of the forecasts results in a unified prediction that supports aligned decisions at different planning horizons: from short-term operational up to long-term strategic planning. The proposed methodology is independent of forecasting models. It can embed high level managerial forecasts that incorporate complex and unstructured information with lower level statistical forecasts. Our results show that forecasting with temporal hierarchies increases accuracy over conventional forecasting, particularly under increased modelling uncertainty. We discuss organisational implications of the temporally reconciled forecasts using a case study of Accident \& Emergency departments

Forecasting COVID-19 with Temporal Hierarchies and Ensemble Methods

Infectious disease forecasting efforts underwent rapid growth during the COVID-19 pandemic, providing guidance for pandemic response and about potential future trends. Yet despite their importance, short-term forecasting models often struggled to produce accurate real-time predictions of this complex and rapidly changing system. This gap in accuracy persisted into the pandemic and warrants the exploration and testing of new methods to glean fresh insights. In this work, we examined the application of the temporal hierarchical forecasting (THieF) methodology to probabilistic forecasts of COVID-19 incident hospital admissions in the United States. THieF is an innovative forecasting technique that aggregates time-series data into a hierarchy made up of different temporal scales, produces forecasts at each level of the hierarchy, then reconciles those forecasts using optimized weighted forecast combination. While THieF\u27s unique approach has shown substantial accuracy improvements in a diverse range of applications, such as operations management and emergency room admission predictions, this technique had not previously been applied to outbreak forecasting. We generated candidate models formulated using the THieF methodology, which differed by their hierarchy schemes and data transformations, and ensembles of the THieF models, computed as a mean of predictive quantiles. The models were evaluated using weighted interval score (WIS) as a measure of forecast skill, and the top-performing subset was compared to several benchmark models. These models included simple ARIMA and seasonal ARIMA models, a naive baseline model, and an ensemble of operational incident hospitalization models from the US COVID-19 Forecast Hub. The THieF models and THieF ensembles demonstrated improvements in WIS and MAE, as well as competitive prediction interval coverage, over many benchmark models for both the validation and testing phases. The best THieF model generally ranked second out of nine total models during the testing evaluation. These accuracy improvements suggest the THieF methodology may serve as a useful addition to the infectious disease forecasting toolkit

Hierarchical learning, forecasting coherent spatio-temporal individual and aggregated building loads

Optimal decision-making compels us to anticipate the future at different horizons. However, in many domains connecting together predictions from multiple time horizons and abstractions levels across their organization becomes all the more important, else decision-makers would be planning using separate and possibly conflicting views of the future. This notably applies to smart grid operation. To optimally manage energy flows in such systems, accurate and coherent predictions must be made across varying aggregation levels and horizons. With this work, we propose a novel multi-dimensional hierarchical forecasting method built upon structurally-informed machine-learning regressors and established hierarchical reconciliation taxonomy. A generic formulation of multi-dimensional hierarchies, reconciling spatial and temporal hierarchies under a common frame is initially defined. Next, a coherency-informed hierarchical learner is developed built upon a custom loss function leveraging optimal reconciliation methods. Coherency of the produced hierarchical forecasts is then secured using similar reconciliation technics. The outcome is a unified and coherent forecast across all examined dimensions. The method is evaluated on two different case studies to predict building electrical loads across spatial, temporal, and spatio-temporal hierarchies. Although the regressor natively profits from computationally efficient learning, results displayed disparate performances, demonstrating the value of hierarchical-coherent learning in only one setting. Yet, supported by a comprehensive result analysis, existing obstacles were clearly delineated, presenting distinct pathways for future work. Overall, the paper expands and unites traditionally disjointed hierarchical forecasting methods providing a fertile route toward a novel generation of forecasting regressors

Hierarchical Forecasting at Scale

Existing hierarchical forecasting techniques scale poorly when the number of time series increases. We propose to learn a coherent forecast for millions of time series with a single bottom-level forecast model by using a sparse loss function that directly optimizes the hierarchical product and/or temporal structure. The benefit of our sparse hierarchical loss function is that it provides practitioners a method of producing bottom-level forecasts that are coherent to any chosen cross-sectional or temporal hierarchy. In addition, removing the need for a post-processing step as required in traditional hierarchical forecasting techniques reduces the computational cost of the prediction phase in the forecasting pipeline. On the public M5 dataset, our sparse hierarchical loss function performs up to 10% (RMSE) better compared to the baseline loss function. We implement our sparse hierarchical loss function within an existing forecasting model at bol, a large European e-commerce platform, resulting in an improved forecasting performance of 2% at the product level. Finally, we found an increase in forecasting performance of about 5-10% when evaluating the forecasting performance across the cross-sectional hierarchies that we defined. These results demonstrate the usefulness of our sparse hierarchical loss applied to a production forecasting system at a major e-commerce platform

Cross-temporal forecast reconciliation: Optimal combination method and heuristic alternatives

Forecast reconciliation is a post-forecasting process aimed to improve the quality of the base forecasts for a system of hierarchical/grouped time series (Hyndman et al., 2011). Contemporaneous (cross-sectional) and temporal hierarchies have been considered in the literature, but - except for Kourentzes and Athanasopoulos (2019) - generally these two features have not been fully considered together. Adopting a notation able to simultaneously deal with both forecast reconciliation dimensions, the paper shows two new results: (i) an iterative cross-temporal forecast reconciliation procedure which extends, and overcomes some weaknesses of, the two-step procedure by Kourentzes and Athanasopoulos (2019), and (ii) the closed-form expression of the optimal (in least squares sense) point forecasts which fulfill both contemporaneous and temporal constraints. The feasibility of the proposed procedures, along with first evaluations of their performance as compared to the most performing `single dimension' (either cross-sectional or temporal) forecast reconciliation procedures, is studied through a forecasting experiment on the 95 quarterly time series of the Australian GDP from Income and Expenditure sides considered by Athanasopoulos et al. (2019).Comment: Main text: 49 pages, 10 figures, 2 tables. Appendix: 68 pages, 29 figures, 17 table

Rethinking Sensors Modeling: Hierarchical Information Enhanced Traffic Forecasting

With the acceleration of urbanization, traffic forecasting has become an essential role in smart city construction. In the context of spatio-temporal prediction, the key lies in how to model the dependencies of sensors. However, existing works basically only consider the micro relationships between sensors, where the sensors are treated equally, and their macroscopic dependencies are neglected. In this paper, we argue to rethink the sensor's dependency modeling from two hierarchies: regional and global perspectives. Particularly, we merge original sensors with high intra-region correlation as a region node to preserve the inter-region dependency. Then, we generate representative and common spatio-temporal patterns as global nodes to reflect a global dependency between sensors and provide auxiliary information for spatio-temporal dependency learning. In pursuit of the generality and reality of node representations, we incorporate a Meta GCN to calibrate the regional and global nodes in the physical data space. Furthermore, we devise the cross-hierarchy graph convolution to propagate information from different hierarchies. In a nutshell, we propose a Hierarchical Information Enhanced Spatio-Temporal prediction method, HIEST, to create and utilize the regional dependency and common spatio-temporal patterns. Extensive experiments have verified the leading performance of our HIEST against state-of-the-art baselines. We publicize the code to ease reproducibility.Comment: 9 pages, accepted by CIKM'2

Cross-temporal aggregation: Improving the forecast accuracy of hierarchical electricity consumption

Achieving high accuracy in load forecasting requires the selection of appropriate forecasting models, able to capture the special characteristics of energy consumption time series. When hierarchies of load from different sources are considered together, the complexity increases further; for example, when forecasting both at system and region level. Not only the model selection problem is expanded to multiple time series, but we also require aggregation consistency of the forecasts across levels. Although hierarchical forecast can address the aggregation consistency concerns, it does not resolve the model selection uncertainty. To address this we rely on Multiple Temporal Aggregation, which has been shown to mitigate the model selection problem for low frequency time series. We propose a modification for high frequency time series and combine conventional cross-sectional hierarchical forecasting with multiple temporal aggregation. The effect of incorporating temporal aggregation in hierarchical forecasting is empirically assessed using a real data set from five bank branches, demonstrating superior accuracy, aggregation consistency and reliable automatic forecasting

Cross-temporal aggregation: Improving the forecast accuracy of hierarchical electricity consumption

Achieving high accuracy in load forecasting requires the selection of appropriate forecasting models, able to capture the special characteristics of energy consumption time series. When hierarchies of load from different sources are considered together, the complexity increases further; for example, when forecasting both at system and region level. Not only the model selection problem is expanded to multiple time series, but we also require aggregation consistency of the forecasts across levels. Although hierarchical forecast can address the aggregation consistency concerns, it does not resolve the model selection uncertainty. To address this we rely on Multiple Temporal Aggregation, which has been shown to mitigate the model selection problem for low frequency time series. We propose a modification for high frequency time series and combine conventional cross-sectional hierarchical forecasting with multiple temporal aggregation. The effect of incorporating temporal aggregation in hierarchical forecasting is empirically assessed using a real data set from five bank branches, demonstrating superior accuracy, aggregation consistency and reliable automatic forecasting