Hierarchical Forecasting Research Articles

The practicality of Malaysia dengue outbreak forecasting model as an early warning system.

Dengue is a harmful tropical disease that causes death to many people. Currently, the dengue vaccine development is still at an early stage, and only intervention methods exist after dengue cases increase. Thus, previously, two scientific experimental field studies were conducted in producing a dengue outbreak forecasting model as an early warning system. Successfully, an Autoregressive Distributed Lag (ADL) Model was developed using three factors: the epidemiological, entomological, and environmental with an accuracy of 85%; but a higher percentage is required in minimizing the error for the model to be useful. Hence, this study aimed to develop a practical and cost-effective dengue outbreak forecasting model with at least 90% accuracy to be embedded in an early warning computer system using the Internet of Things (IoT) approach. Eighty-one weeks of time series data of the three factors were used in six forecasting models, which were Autoregressive Distributed Lag (ADL), Hierarchical Forecasting (Bottom-up and Optimal combination) and three Machine Learning methods: (Artificial Neural Network (ANN), Support Vector Machine (SVM) and Random Forest). Five error measures were used to evaluate the consistency performance of the models in order to ensure model performance. The findings indicated Random Forest outperformed the other models with an accuracy of 95% when including all three factors. But practically, collecting mosquito related data (the entomological factor) was very costly and time consuming. Thus, it was removed from the model, and the accuracy dropped to 92% but still high enough to be of practical use, i.e., beyond 90%. However, the practical ground operationalization of the early warning system also requires several rain gauges to be located at the dengue hot spots due to localized rainfall. Hence, further analysis was conducted in determining the location of the rain gauges. This has led to the recommendation that the rain gauges should be located about 3–4 km apart at the dengue hot spots to ensure the accuracy of the rainfall data to be included in the dengue outbreak forecasting model so that it can be embedded in the early warning system. Therefore, this early warning system can save lives, and prevention is better than cure.

A multi-scale time-series dataset with benchmark for machine learning in decarbonized energy grids

The electric grid is a key enabling infrastructure for the ambitious transition towards carbon neutrality as we grapple with climate change. With deepening penetration of renewable resources, the reliable operation of the electric grid becomes increasingly challenging. In this paper, we present PSML, a first-of-its-kind open-access multi-scale time-series dataset, to aid in the development of data-driven machine learning (ML)-based approaches towards reliable operation of future electric grids. The dataset is synthesized from a joint transmission and distribution electric grid to capture the increasingly important interactions and uncertainties of the grid dynamics, containing power, voltage and current measurements over multiple spatio-temporal scales. Using PSML, we provide state-of-the-art ML benchmarks on three challenging use cases of critical importance to achieve: (i) early detection, accurate classification and localization of dynamic disturbances; (ii) robust hierarchical forecasting of load and renewable energy; and (iii) realistic synthetic generation of physical-law-constrained measurements. We envision that this dataset will provide use-inspired ML research in safety-critical systems, while simultaneously enabling ML researchers to contribute towards decarbonization of energy sectors.

Bayesian Optimization and Hierarchical Forecasting of Non-Weather-Related Electric Power Outages

Power outage prediction is important for planning electric power system response, restoration, and maintenance efforts. It is important for utility managers to understand the impact of outages on the local distribution infrastructure in order to develop appropriate maintenance and resilience measures. Power outage prediction models in literature are often limited in scope, typically tailored to model extreme weather related outage events. While these models are sufficient in predicting widespread outages from adverse weather events, they may fail to capture more frequent, non-weather related outages (NWO). In this study, we explore time series models of NWO by incorporating state-of-the-art techniques that leverage the Prophet model in Bayesian optimization and hierarchical forecasting. After defining a robust metric for NWO (non-weather outage count index, NWOCI), time series forecasting models that leverage advanced preprocessing and forecasting techniques in Kats and Prophet, respectively, were built and tested using six years of daily state- and county-level outage data in Massachusetts (MA). We develop a Prophet model with Bayesian True Parzen Estimator optimization (Prophet-TPE) using state-level outage data and a hierarchical Prophet-Bottom-Up model using county-level data. We find that these forecasting models outperform other Bayesian and hierarchical model combinations of Prophet and Seasonal Autoregressive Integrated Moving Average (SARIMA) models in predicting NWOCI at both county and state levels. Our time series trend decomposition reveals a concerning trend in the growth of NWO in MA. We conclude with a discussion of these observations and possible recommendations for mitigating NWO.

Model selection in reconciling hierarchical time series

Model selection has been proven an effective strategy for improving accuracy in time series forecasting applications. However, when dealing with hierarchical time series, apart from selecting the most appropriate forecasting model, forecasters have also to select a suitable method for reconciling the base forecasts produced for each series to make sure they are coherent. Although some hierarchical forecasting methods like minimum trace are strongly supported both theoretically and empirically for reconciling the base forecasts, there are still circumstances under which they might not produce the most accurate results, being outperformed by other methods. In this paper we propose an approach for dynamically selecting the most appropriate hierarchical forecasting reconciliation method and leading to more accurate coherent forecasts. The approach, which we call conditional hierarchical forecasting, is based on machine learning classification methods that use time series features to select the reconciliation method for each hierarchy. Moreover, it allows the selection to be tailored according to the accuracy measure of preference and the hierarchical level(s) of interest. Our results suggest that conditional hierarchical forecasting can lead to significantly more accurate forecasts than standard approaches, especially at lower hierarchical levels.

Demand forecasting in supply chains: a review of aggregation and hierarchical approaches

Demand forecasts are the basis of most decisions in supply chain management. The granularity of these decisions lead to different forecast requirements. For example, inventory replenishment decisions require forecasts at the individual SKU level over lead time, whereas forecasts at higher levels, over longer horizons, are required for supply chain strategic decisions. The most accurate forecasts are not always obtained from data at the 'natural' level of aggregation. In some cases, forecast accuracy may be improved by aggregating data or forecasts at lower levels, or disaggregating data or forecasts at higher levels, or by combining forecasts at multiple levels of aggregation. Temporal and cross-sectional aggregation approaches are well established in the literature. More recently, it has been argued that these two approaches do not make the fullest use of data available at the different hierarchical levels of the supply chain. Therefore, consideration of forecasting hierarchies (over time and other dimensions), and combinations of forecasts across hierarchical levels, have been recommended. This paper provides a comprehensive review of research dealing with aggregation and hierarchical forecasting in supply chains, based on a systematic search. The review enables the identification of major research gaps and the presentation of an agenda for further research.

Research on an ionospheric delay correction method for the interferometric imaging radar altimeter based on improved GIM data

ABSTRACT The Interferometric Imaging Radar Altimeter (InIRA) is alow-orbit single-frequency altimeter whose signals are subject to an ionospheric delay, which introduces measurement errors. Additionally, some difficulties, such as selecting the interpolation algorithm and intercepting the height scale, arise when applying the ionospheric correction model. Based on Sentinel-3A dual-frequency measurements, this paper suggests that linear variogram-based kriging is suitable for spatial interpolation, and the total electron content height scale coefficient calculated by the hierarchical IRI forecast model can be applied to the interpolated GIM intercept. When the improved GIM value is applied to four scenes of InIRA data, the obtained Ku-band ionospheric correction varies from 1.49cm to 1.57cm.

Transfer learning for hierarchical forecasting: Reducing computational efforts of M5 winning methods

The winning machine learning methods of the M5 Accuracy competition demonstrated high levels of forecast accuracy compared to the top-performing benchmarks in the history of the M-competitions. Yet, large-scale adoption is hampered due to the significant computational requirements to model, tune, and train these state-of-the-art algorithms. To overcome this major issue, we discuss the potential of transfer learning (TL) to reduce the computational effort in hierarchical forecasting and provide a proof of concept that TL can be applied on M5 top-performing methods. We demonstrate our easy-to-use TL framework on the recursive store-level LightGBM models of the M5 winning method and attain similar levels of forecast accuracy with roughly 25% less training time. Our findings provide evidence for a novel application of TL to facilitate the practical applicability of the M5 winning methods in large-scale settings with hierarchically structured data.

Hierarchical forecast reconciliation with machine learning

Over the last 15 years, studies on hierarchical forecasting have moved away from single-level approaches towards proposing linear combination approaches across multiple levels of the hierarchy. Such combinations offer coherent reconciled forecasts, improved forecasting performance and aligned decision-making. This paper proposes a novel hierarchical forecasting approach based on machine learning. The proposed method allows for non-linear combinations of the base forecasts, thus being more general than linear approaches. We structurally combine the objectives of improved post-sample empirical forecasting accuracy and coherence. Due to its non-linear nature, our approach selectively combines the base forecasts in a direct and automated way without requiring that the complete information must be used for producing reconciled forecasts for each series and level. The proposed method is evaluated both in terms of accuracy and bias using two different data sets coming from the tourism and retail industries. Our results suggest that the proposed method gives superior point forecasts than existing approaches, especially when the series comprising the hierarchy are not characterized by the same patterns.

Stochastic coherency in forecast reconciliation

Hierarchical forecasting has been receiving increasing attention in the literature. The notion of coherency is central to this, which implies that the hierarchical time series follows some linear aggregation constraints. This notion, however, does not take several modelling uncertainties into account. We propose to redefine coherency as stochastic. This allows to accommodate overlooked uncertainties in forecast reconciliation. We show analytically that there are two potential sources of uncertainty in forecast reconciliation. We use simulated data to demonstrate how these uncertainties propagate to the covariance matrix estimation, introducing uncertainty in the reconciliation weights matrix. This then increases the uncertainty of the reconciled forecasts. We apply our understanding to modelling accident and emergency admissions in a UK hospital. Our analysis confirms the insights from stochastic coherency in forecast reconciliation. It shows that we gain accuracy improvement from forecast reconciliation, on average, at the cost of the variability of the forecast error distribution. Users may opt to prefer less volatile error distributions to assist decision making.

Deep LSTM-Based Transfer Learning Approach for Coherent Forecasts in Hierarchical Time Series.

Hierarchical time series is a set of data sequences organized by aggregation constraints to represent many real-world applications in research and the industry. Forecasting of hierarchical time series is a challenging and time-consuming problem owing to ensuring the forecasting consistency among the hierarchy levels based on their dimensional features. The excellent empirical performance of our Deep Long Short-Term Memory (DLSTM) approach on various forecasting tasks motivated us to extend it to solve the forecasting problem through hierarchical architectures. Toward this target, we develop the DLSTM model in auto-encoder (AE) fashion and take full advantage of the hierarchical architecture for better time series forecasting. DLSTM-AE works as an alternative approach to traditional and machine learning approaches that have been used to manipulate hierarchical forecasting. However, training a DLSTM in hierarchical architectures requires updating the weight vectors for each LSTM cell, which is time-consuming and requires a large amount of data through several dimensions. Transfer learning can mitigate this problem by training first the time series at the bottom level of the hierarchy using the proposed DLSTM-AE approach. Then, we transfer the learned features to perform synchronous training for the time series of the upper levels of the hierarchy. To demonstrate the efficiency of the proposed approach, we compare its performance with existing approaches using two case studies related to the energy and tourism domains. An evaluation of all approaches was based on two criteria, namely, the forecasting accuracy and the ability to produce coherent forecasts through through the hierarchy. In both case studies, the proposed approach attained the highest accuracy results among all counterparts and produced more coherent forecasts.

Hierarchical forecasts of Diabetes mortality in Mexico by marginalization and sex to establish resource allocation

Objective: The mexican population has experimented an astounding rise in type II Diabetes mortality as well as a growing trend for the economic burden in the recent years. The paper’s purpose is to propose an approach to establish a distribution of resource allocation objectively to face the future economic burden. Methodology: Hierarchical forecasts of Diabetes mortality to 2030 by sub-domains of the population are estimated based on marginalization and sex. Results: The forecasts confirm that differences related to sub-domains will be significant. In fact, the rates will increase most notably both in low and high marginalized. Limitations: The hierarchical method just provide point forecast without prediction intervals. Originality: There is not a similar application for Mexican data to do that objectively. Conclusions: The most recommendable budget distribution should be mainly addressed among the low and high levels. Implications of these estimates should support unpostponable health policy in general and for the mentioned sub-domains in particular. Recepción: 25/10/2020 Aceptación: 10/03/2021

A machine learning approach for forecasting hierarchical time series

In this paper, we propose a machine learning approach for forecasting hierarchical time series. When dealing with hierarchical time series, apart from generating accurate forecasts, one needs to select a suitable method for producing reconciled forecasts. Forecast reconciliation is the process of adjusting forecasts to make them coherent across the hierarchy. In literature, coherence is often enforced by using a post-processing technique on the base forecasts produced by suitable time series forecasting methods. On the contrary, our idea is to use a deep neural network to directly produce accurate and reconciled forecasts. We exploit the ability of a deep neural network to extract information capturing the structure of the hierarchy. We impose the reconciliation at training time by minimizing a customized loss function. In many practical applications, besides time series data, hierarchical time series include explanatory variables that are beneficial for increasing the forecasting accuracy. Exploiting this further information, our approach links the relationship between time series features extracted at any level of the hierarchy and the explanatory variables into an end-to-end neural network providing accurate and reconciled point forecasts. The effectiveness of the approach is validated on three real-world datasets, where our method outperforms state-of-the-art competitors in hierarchical forecasting.

Forecasting with Deep Temporal Hierarchies

In time series analysis and forecasting, the identification of an appropriate model remains a challenging task. Model misspecification can lead to erroneous forecasts and insights. The use of multiple views of the same time series by constructing temporally aggregate levels has been proposed as a way to overcome the model specification and selection uncertainty, with ample empirical evidence of forecast accuracy gains. Temporal Hierarchies is the most popular approach to achieve this, which itself is based on research in hierarchical forecasting. Although there has been substantial progress in this literature, the vast majority of methods rely on a restricted linear combination of different model outputs across the hierarchy. We investigate the use of deep learning to augment temporal hierarchies, relaxing the classical restrictions. Specifically, we look at deep learning for the generation of all the base forecasts, the hierarchical reconciliation, and an end-to-end method that embeds all steps in a single neural network. We inspect the performance of the proposed methods when applied to individual time series, or with global training across complete sets of series. We further investigate the requirements in terms of series set size, illustrating the conditions where deep learning temporal hierarchies outperform conventional temporal hierarchies.

A Survey of Computational Intelligence Techniques for Wind Power Uncertainty Quantification in Smart Grids.

The high penetration level of renewable energy is thought to be one of the basic characteristics of future smart grids. Wind power, as one of the most increasing renewable energy, has brought a large number of uncertainties into the power systems. These uncertainties would require system operators to change their traditional ways of decision-making. This article provides a comprehensive survey of computational intelligence techniques for wind power uncertainty quantification in smart grids. First, prediction intervals (PIs) are introduced as a means to quantify the uncertainties in wind power forecasts. Various PI evaluation indices, including the latest trends in comprehensive evaluation techniques, are compared. Furthermore, computational intelligence-based PI construction methods are summarized and classified into traditional methods (parametric) and direct PI construction methods (nonparametric). In the second part of this article, methods of incorporating wind power forecast uncertainties into power system decision-making processes are investigated. Three techniques, namely, stochastic models, fuzzy logic models, and robust optimization, and different power system applications using these techniques are reviewed. Finally, future research directions, such as spatiotemporal and hierarchical forecasting, deep learning-based methods, and integration of predictive uncertainty estimates into the decision-making process, are discussed. This survey can benefit the readers by providing a complete technical summary of wind power uncertainty quantification and decision-making in smart grids.

Reconciling solar forecasts: Probabilistic forecasting with homoscedastic Gaussian errors on a geographical hierarchy

Hierarchical forecasting and reconciliation are new to the field of solar engineering. Previous papers in this series, namely, Yang et al. (2017a, 2017b), and Yagli et al. (2019b), discussed various reconciliation techniques for deterministic solar forecasts obtained across spatio-temporal hierarchies. This paper extends the discussion into probability space, and studies how reconciliation can affect the performance of probabilistic forecasting. More specifically, qualities of the parametric predictive distributions before and after reconciliation are compared.Four minimum-trace-based reconciliation techniques are used to reconcile day-ahead and hour-ahead forecasts generated using two datasets: (1) distributed solar power generation for 318 simulated PV systems in California, and (2) satellite-derived irradiance over Arizona. The empirical result shows that reconciliation not only improves the accuracy of point forecasts, but also leads to high-quality predictive distributions in terms of sharpness, calibration, and skill score. Moreover, such improvement is quite general, and does not seem to depend on data, hierarchy structure, nor the underlying forecasting model.

Hierarchy and Performance of Analyst Teams

We examine the effect of hierarchy on analyst teams’ performance using a large sample of financial analysts from China. Hierarchy, defined as the disparity in power or status within a group, which we operationalize as the difference in experience between the senior and junior analyst in a team, is an important aspect of team structure that could affect team performance. We find that analyst teams with a hierarchy outperform flat teams (teams without a clear hierarchy). Specifically, hierarchical teams issue forecasts with higher accuracy, less optimism bias, less co-movement with the consensus, and stronger investor reactions. The results remain robust after we control for a number of firm and analyst characteristics and fixed effects. Further analysis shows that working in a hierarchical team helps junior analysts improve their individual forecasts for other firms, and senior analysts also benefit from working with junior analysts in hierarchical teams. Our results provide important insights into understanding the effect of team structure on the performance of analyst teams who issue majority of earnings forecasts.

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

Achieving high accuracy in energy consumption forecasting is critical for improving energy management and planning. However, this requires the selection of appropriate forecasting models, able to capture the individual characteristics of the series to be predicted, which is a task that involves a lot of uncertainty. When hierarchies of load from different sources are considered together, the uncertainty and complexity increase 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 forecasting, such as the bottom-up, the top-down, and the optimal reconciliation methods, can address the aggregation consistency concerns, it does not resolve the model selection uncertainty. To address this issue, we rely on Multiple Temporal Aggregation (MTA), which has been shown to mitigate the model selection problem for low-frequency time series. We propose a modification of the Multiple Aggregation Prediction Algorithm, a special implementation of MTA, for high-frequency time series to better handle the undesirable effect of seasonality shrinkage that MTA implies and combine it with conventional cross-sectional hierarchical forecasting. The impact of incorporating temporal aggregation in hierarchical forecasting is empirically assessed using a real data set from five bank branches. We show that the proposed MTA approach, combined with the optimal reconciliation method, demonstrates superior accuracy, aggregation consistency, and reliable automatic forecasting.

Study on Early Warning Method for Water Inrush in Tunnel Based on Fine Risk Evaluation and Hierarchical Advance Forecast

Water inrush is one of the most frequent and harmful geological disasters in tunnel construction. In order to effectively prevent and control the occurrence of water inrush, an early warning method based on fine risk evaluation and hierarchical advanced forecast is proposed. Water inrush is a complex dynamic coupling factors system, the relationship between influencing factors and water inrush is strongly nonlinear. Therefore, the efficacy coefficient model, which has the advantages of standardization, conciseness, and freedom from subjective factors, is improved nonlinearly. The fine risk evaluation theory and method based on the improved efficacy coefficient model consisted of two parts: one is static evaluation used in design stage, and the other is dynamic evaluation applied in the construction stage. The index weights are determined scientifically and reasonably by Analytical Hierarchy Process (AHP) and the entropy method. According to the fine risk evaluation results, combined with the advantages and disadvantages of various forecasting methods, a multistep hierarchical detection method of disaster resources for water inrush is proposed to identify the occurrence characteristics and failure level of disaster sources. The theory has been successfully applied to the #3 inclined well of Yuelongmen Tunnel in Cheng-Lan Railway. The evaluation results had good agreement with the actual excavation data, which indicates that the model is of high credibility and feasibility. The method could improve the prediction accuracy of water inrush and explore geometric characteristics and filling of disaster-causing structures. It is of great significance for avoiding water inrush and guiding the rapid and safe tunnel construction.

A bottom-up hierarchical forecasting of broadband penetration in India using ARIMA & DES approaches

A bottom-up hierarchical forecasting of broadband penetration in India using ARIMA & DES approaches

Supply chain decision support systems based on a novel hierarchical forecasting approach

Time series forecasting plays an important role in many decision support systems, also in those related to the management of supply chains. Forecast accuracy is, therefore, essential to optimise the efficiency of any supply chain. One aspect that is often overlooked is the fact that sales of many products within an organization are assembled as complex hierarchies with different levels of aggregation. Very often forecasts are produced regardless of such structure, though forecasting accuracy may be improved by taking it into account. In this paper, an approach for hierarchical time series forecasting based on State Space modelling is proposed. Previous developments provide solutions to the hierarchical forecasting problem by algebra manipulations based on forecasts produced by independent models for each time series involved in the hierarchy. The solutions produce optimal reconciled forecasts for each individual forecast horizon, but the link along time that is implied by the dynamics of the models is completely ignored. Therefore, the novel approach in this paper improves upon past research at least in two key points. Firstly, the algebra is already encoded in the State Space system and the Kalman Filter algorithm, giving an elegant and clean solution to the problem. Secondly, the State Space approach is optimal both across the hierarchy, as expected, but also along time, something missing in past developments. The approach is assessed by comparing its forecasting performance to the existing methods, through simulations and using real data of a Spanish grocery retailer.