This dissertation comprises of three original contributions to empirical forecasting research. Chapter 1 introduces the dissertation. Chapter 2 contributes to the literature on hierarchical time series (HTS) modelling by proposing a disaggregated forecasting system for both inflation rate and its volatility. Using monthly data that underlies the Retail Prices Index for the UK, we analyse the dynamics of the inflation process. We examine patterns in the time-varying covariation among product-level inflation rates that aggregate up to industry-level inflation rates that in turn aggregate up to the overall inflation rate. The aggregate inflation volatility closely tracks the time path of this covariation, which is seen to be driven primarily by the variances of common shocks shared by all products, and by the covariances between idiosyncratic product-level shocks. We formulate a forecasting system that comprises of models for mean inflation rate and its variance, and exploit the index structure of the aggregate inflation rate using the HTS framework. Using a dynamic model selection approach to forecasting, we obtain forecasts that are between 9 and 155 % more accurate than a SARIMA-GARCH(1,1) for the aggregate inflation volatility. Chapter 3 is on improving forecasts using forecast combinations. The paper documents the software implementation of the open source R package for forecast combination that we coded and published on the official R package depository, CRAN. The GeomComb package is the only R package that covers a wide range of different popular forecast combination methods. We implement techniques from 3 broad categories: (a) simple non-parametric methods, (b) regression-based methods, and (c) geometric (eigenvector) methods, allowing for static or dynamic estimation of each approach. Using S3 classes/methods in R, the package provides a user-friendly environment for applied forecasting, implementing solutions for typical issues related to forecast combination (multicollinearity, missing values, etc.), criterion-based optimisation for several parametric methods, and post-fit functions to rationalise and visualise estimation results. The package has been listed in the official R Task Views for Time Series Analysis and for Official Statistics. The brief empirical application in the paper illustrates the package’s functionality by estimating forecast combination techniques for monthly UK electricity supply. Chapter 4 introduces HTS forecasting and forecast combination to a healthcare staffing context. A slowdown of healthcare budget growth in the UK that does not keep pace with growth of demand for hospital services made efficient cost planning increasingly crucial for hospitals, in particular for staff which accounts for more than half of hospitals’ expenses. This is facilitated by accurate forecasts of patient census and churn. Using a dataset of more than 3 million observations from a large UK hospital, we show how HTS forecasting can improve forecast accuracy by using information at different levels of the hospital hierarchy (aggregate, emergency/electives, divisions, specialties), compared to the naïve benchmark: the seasonal random walk model applied to the aggregate. We show that forecast combination can improve accuracy even more in some cases, and leads to lower forecast error variance (decreasing forecasting risk). We propose a comprehensive parametric approach to use forecasts in a nurse staffing model that has the aim of minimising cost while satisfying that the care requirements (e.g. nurse hours per patient day thresholds) are met.

Temporal hierarchies are being increasingly used for forecasting purposes over the past years. They have been shown to produce accurate and coherent forecasts which are beneficial for enterprises. Reconciling forecasts of different aggregation levels to achieve coherence, supports aligned decisions between different organizational levels. Current research focuses on analytical reconciliation methods which have shown to be more beneficial than conventional Bottom-Up and Top-Down approaches. However, such methods rely on a number of assumptions, primarily due to estimation requirements. This work proposes a novel approach for forecasting with temporal hierarchies. It results in a non-linear reconciliation method inspired by the architecture of an encoder-decoder deep neural network. A trainable encoder combines base forecasts into the reconciled bottom level predictions, while a fixed, non-trainable decoder reconstructs the forecasts across all hierarchical levels. Two different reconciliation architectures are presented based on different optimization procedures. They both ensure coherence. This thesis suggests two alternative usages for the reconcilers. One, to replace analytical expressions and reconcile base forecasts produced by models such as Exponential Smoothing. Second, as a part of a deep neural architecture DTH-28, which mimics the general framework for forecasting with temporal hierarchies. The proposed framework outperforms established benchmarks on real data. Furthermore, this work discusses the general effect of coherence on forecast accuracy. Coherence affects accuracy in two ways. One as a regularizer and second as a stepwise function. Exploiting each usage offers different accuracy benefits.

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's 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.

[pt] Séries Temporais que podem ser organizadas em níveis de acordo com, por exemplo, o tipo de produto, região geográfica, classe de consumo, dentre outros, são chamadas de Séries Temporais Hierárquicas (ou agrupadas, quando possuem mais de uma variável de agregação). Informações referentes à previsão destas séries são fundamentais para a tomada de decisão seja no nível gerencial ou operacional de todo tipo de negócio. Para atender a essas informações, são utilizadas técnicas de previsão hierárquica, que têm como foco reduzir os custos e melhorar a acurácia da previsão. O objetivo deste trabalho é estudar abordagens para agregar/desagregar previsões feitas para Séries Temporais Hierárquicas ou Agrupadas. Como resultado do trabalho destaca-se a apresentação das abordagens que representam o estado da arte em previsão hierárquica: Reconciliação Ótima (também chamada de Combinação Ótima) e Top-Down baseada na Proporção das Previsões. Ainda referente aos resultados destaca-se a análise das diversas técnicas de previsão hierárquica encontradas na literatura aplicadas a duas séries clássicas do contexto brasileiro: a série agrupada de consumo de energia elétrica agregada por região do país e classe de consumo, e a série hierárquica de demanda de transporte aéreo representada pela variável RPK (Revenue Passenger Kilometers). O desempenho preditivo das abordagens foi avaliado com base na métrica MAPE, e o teste de Diebold-Mariano foi aplicado para verificar se a diferença no desempenho das abordagens novas e tradicionais é significativa. / [en] Time Series which can be arranged in levels according to, for example, the type of product, geography, consumption class, among others, are called Hierarchical Time Series (or grouped, if they have more than one aggregation variable). Information relating these series prediction is fundamental for decision-making at the management or operational level of all types of business. To meet these information, hierarchical forecasting techniques are used, which are focused on reducing costs and improving the accuracy of prediction. The objective of this work is to study approaches to aggregate / disaggregate predictions for Hierarchical or Grouped Time Series. As a result of the work there is the presentation of the approaches that represent the state of the art hierarchical forecast: Optimal Reconciliation approach (also called the Optimal Combination) and Top-Down Forecast Proportions approach. Still on the results highlight the analysis of the various hierarchical forecasting techniques found in the literature applied to two classic series of the Brazilian context: a grouped series of electricity consumption aggregated by region of the country and consumer class, and the hierarchical series air transport demand represented by the variable RPK (Revenue Passenger Kilometers). The predictive performance of the approaches was evaluated based on the metric MAPE and the Diebold-Mariano test was used to verify that the difference in performance of new and traditional approaches is significant.

[pt] Tendo em vista mudanças significativas no varejo causadas pelo crescimento de compras online no Brasil, este estudo tem como objetivo facilitar um relevante lead time e um forte grau de assertividade na previsão de demanda do Omnichannel de uma empresa do setor. Com a crescente relevância do Omnichannel, é importante compreender as necessidades dos consumidores tradicionais e digitais, integrar suas experiências e oferecer múltiplos canais de compra. Nesse contexto, a previsão de demanda é crucial para apoiar as decisões estratégicas, táticas e operacionais da organização. A utilização de séries temporais hierárquicas auxilia na precisão das previsões e, portanto, na tomada de decisões, permitindo gerar estimativas coerentes ao longo dos múltiplos níveis hierárquicos. Dessa forma, neste estudo, combinando as metodologias de previsão de séries temporais ETS, ARIMA e SARIMAX, com métodos de reconciliação Bottom-up, Top-down, MinTrace Combinação Ótima (OLS) e MinTrace WLS Struct, doze modelos foram gerados. Baseado nas principais abordagens de séries temporais hierárquicas, com uma sequência de sete passos, os modelos foram comparados, por meio de métricas de avaliação de desempenho, para identificar qual deles melhor se encaixa na série trabalhada. Ao final do estudo, o modelo SARIMAX com Bottom-up se mostrou a combinação mais adequada para a série em análise. A abordagem alcançou um MAPE de 22 por cento no nível mais agregado da hierarquia, reduzindo em cinco pontos percentuais o MAPE original da empresa, além de apresentar a melhor colocação na combinação das métricas comparativamente. / [en] In light of recent changes in retail caused by the growth of online shopping in Brazil, this study aims to enable a substantial lead time and a high degree of accuracy of the Omnichannel demand forecast for a retail company. As Omnichannel success continues to expand, it becomes increasingly important tounderstand the needs of both traditional and digital consumers, integrate their experiences and offer multiple purchase channels. In this context, demand forecasting is crucial for identifying market trends, growth opportunities, potentialstrategies and supporting strategic, tactical and operational decisions. The use of Hierarchical Time Series improves forecasts accuracy and, therefore, assists in decision-making, allowing the development of consistent estimations acrossmultiple hierarchical levels. Thus, this study combines the time series forecast generation methodologies ETS, ARIMA and SARIMAX, with Bottom-up, Top-down, MinTrace Optimal Combination (OLS) and MinTrace WLS Struct reconciliation methods, resulting in the generation of twelve models. Based on the main theories of Hierarchical Time Series and following a 7-steps sequence, the models were compared using performance evaluation metrics to identify the best fit for the investigated series. The research concludes that the SARIMAX model,together with the Bottom-up strategy, proves to be the most appropriate composition for the Hierarchical Time Series under analysis, as it demonstrates the best performance across the evaluation metrics, reaching a MAPE of 22 percent at the most aggregated level of the hierarchy and reducing the original company forecasting MAPE by five percentage points.

<p>У докторату је предложен је нови модел за утврђивање деагрегационих<br />пропорција у top down методологији за хијерархијско прогнозирање.<br />Како би се утврдили показатељи рада новог приступа, извршена су<br />теоријска (симулациона студија) и емпиријска истраживања (студија<br />случаја) више ешалонског дистрибутивног ланца. Резултати показују да<br />нови приступ значајно превазилази стандардне моделе top down<br />методологије. Такође, у докторату је тестиран и утицај хијерархијских<br />прогноза на логистичке показатеље (просечне залихе и недостатак<br />залиха). Резултати показују да је нови модел остварио најмањи<br />недостатак залиха приликом примене у стратегијама управљања<br />залихама. Поред наведеног, у докторату је тестирано и комбиновање<br />различитих прогноза и истраживање утицаја особина временских серија<br />на прецизност прогнозирања модела за хијерархијско прогнозирање.</p> / <p>U doktoratu je predložen je novi model za utvrđivanje deagregacionih<br />proporcija u top down metodologiji za hijerarhijsko prognoziranje.<br />Kako bi se utvrdili pokazatelji rada novog pristupa, izvršena su<br />teorijska (simulaciona studija) i empirijska istraživanja (studija<br />slučaja) više ešalonskog distributivnog lanca. Rezultati pokazuju da<br />novi pristup značajno prevazilazi standardne modele top down<br />metodologije. Takođe, u doktoratu je testiran i uticaj hijerarhijskih<br />prognoza na logističke pokazatelje (prosečne zalihe i nedostatak<br />zaliha). Rezultati pokazuju da je novi model ostvario najmanji<br />nedostatak zaliha prilikom primene u strategijama upravljanja<br />zalihama. Pored navedenog, u doktoratu je testirano i kombinovanje<br />različitih prognoza i istraživanje uticaja osobina vremenskih serija<br />na preciznost prognoziranja modela za hijerarhijsko prognoziranje.</p> / <p>In this thesis, a new approach for determining disaggregating proportions in<br />the top down hierarchical forecasting methodology is proposed. In order to<br />estimate the accuracy of the proposed approach, the simulation and case<br />study are performed. Results demonstrate that the approach significantly<br />outperforms standard top down approaches. Also, in this reserach the impact<br />of hierarchical forecasts on logistics indicators (average stock and lack of<br />inventory) is researched. The results show that the new model achieved the<br />smallest lack of inventory in inventory management strategies. Likewise, in<br />this research, the ideas of combining the hierarchical forecasting models and<br />quantifying the influence of time series characteristics on the accuracy of<br />hierarchical forecasting models, are tested. The results are encouraging and<br />further researches are needed in order to reveal all possible benefits of<br />proposed ideas.</p>