We study U.S. Treasury yield curve forecasting under distributional uncertainty and recast forecasting as an operations research and managerial decision problem. Rather than minimizing average forecast error, the forecaster selects a decision rule that minimizes worst case expected loss over an ambiguity set of forecast error distributions. To this end, we propose a distributionally robust ensemble forecasting framework that integrates parametric factor models with high dimensional nonparametric machine learning models through adaptive forecast combinations. The framework consists of three machine learning components. First, a rolling window Factor Augmented Dynamic Nelson Siegel model captures level, slope, and curvature dynamics using principal components extracted from economic indicators. Second, Random Forest models capture nonlinear interactions among macro financial drivers and lagged Treasury yields. Third, distributionally robust forecast combination schemes aggregate heterogeneous forecasts under moment uncertainty, penalizing downside tail risk via expected shortfall and stabilizing second moment estimation through ridge regularized covariance matrices. The severity of the worst case criterion is adjustable, allowing the forecaster to regulate the trade off between robustness and statistical efficiency. Using monthly data, we evaluate out of sample forecasts across maturities and horizons from one to twelve months ahead. Adaptive combinations deliver superior performance at short horizons, while Random Forest forecasts dominate at longer horizons. Extensions to global sovereign bond yields confirm the stability and generalizability of the proposed framework.

Although both data availability and the demand for accurate forecasts are increasing, collaboration between stakeholders is often constrained by data ownership and competitive interests. In contrast to recent proposals within cooperative game-theoretical frameworks, we place ourselves in a more general framework, based on prediction markets. There, independent agents trade forecasts of uncertain future events in exchange for rewards. We introduce and analyse a prediction market that (i) accounts for the historical performance of the agents, (ii) adapts to time-varying conditions, while (iii) permitting agents to enter and exit the market at will. The proposed design employs robust regression models to learn the optimal forecasts' combination whilst handling missing submissions. Moreover, we introduce a pay-off allocation mechanism that considers both in-sample and out-of-sample performance while satisfying several desirable economic properties. Case-studies using simulated and real-world data allow demonstrating the effectiveness and adaptability of the proposed market design.

Current work on forecasting emergency department (ED) admissions focuses on disease aggregates or singular disease types. However, given differences in the dynamics of individual diseases, it is unlikely that any single forecasting model would accurately account for each disease and for all time, leading to significant forecast model uncertainty. Yet, forecasting models for ED admissions to-date do not explore the utility of forecast combinations to improve forecast accuracy and stability. It is also unknown whether improvements in forecast accuracy can be yield from (1) incorporating a large number of environmental and anthropogenic covariates or (2) forecasting total ED causes by aggregating cause-specific ED forecasts. To address this gap, we propose high-dimensional forecast combination schemes to combine a large number of forecasting individual models for forecasting cause-specific ED admissions over multiple causes and forecast horizons. We use time series data of ED admissions with an extensive set of explanatory lagged variables at the national level, including meteorological/ambient air pollutant variables and ED admissions of all 16 causes studied. We show that the simple forecast combinations yield forecast accuracies of around 3.81%-23.54% across causes. Furthermore, forecast combinations outperform individual forecasting models, in more than 50% of scenarios (across all ED admission categories and horizons) in a statistically significant manner. Inclusion of high-dimensional covariates and aggregating cause-specific forecasts to provide all-cause ED forecasts provided modest improvements in forecast accuracy. Forecasting cause-specific ED admissions can provide fine-scale forward guidance on resource optimization and pandemic preparedness and forecast combinations can be used to hedge against model uncertainty when forecasting across a wide range of admission categories.

Forecast combination involves using multiple forecasts to create a single, more accurate prediction. Recently, feature-based forecasting has been employed to either select the most appropriate forecasting models or to optimize the weights of their combination. In this paper, we present a multi-task optimization paradigm that focuses on solving both problems simultaneously and enriches current operational research approaches to forecasting. In essence, it incorporates an additional learning and optimization task into the standard feature-based forecasting approach, focusing on the identification of an optimal set of forecasting methods. During the training phase, an optimization model with linear constraints and quadratic objective function is employed to identify accurate and diverse methods for each time series. Moreover, within the training phase, a neural network is used to learn the behavior of that optimization model. Once training is completed the candidate set of methods is identified using the network. The proposed approach elicits the essential role of diversity in feature-based forecasting and highlights the interplay between model combination and model selection when optimizing forecasting ensembles. Experimental results on a large set of series from the M4 competition dataset show that our proposal enhances point forecast accuracy compared to state-of-the-art methods.

Forecast combination integrates information from various sources by consolidating multiple forecast results from the target time series. Instead of the need to select a single optimal forecasting model, this paper introduces a deep learning ensemble forecasting model based on the Dirichlet process. Initially, the learning rate is sampled with three basis distributions as hyperparameters to convert the infinite mixture into a finite one. All checkpoints are collected to establish a deep learning sub-model pool, and weight adjustment and diversity strategies are developed during the combination process. The main advantage of this method is its ability to generate the required base learners through a single training process, utilizing the decaying strategy to tackle the challenge posed by the stochastic nature of gradient descent in determining the optimal learning rate. To ensure the method's generalizability and competitiveness, this paper conducts an empirical analysis using the weekly dataset from the M4 competition and explores sensitivity to the number of models to be combined. The results demonstrate that the ensemble model proposed offers substantial improvements in prediction accuracy and stability compared to a single benchmark model.

Forecast combinations have flourished remarkably in the forecasting community and, in recent years, have become part of the mainstream of forecasting research and activities. Combining multiple forecasts produced from single (target) series is now widely used to improve accuracy through the integration of information gleaned from different sources, thereby mitigating the risk of identifying a single "best" forecast. Combination schemes have evolved from simple combination methods without estimation, to sophisticated methods involving time-varying weights, nonlinear combinations, correlations among components, and cross-learning. They include combining point forecasts and combining probabilistic forecasts. This paper provides an up-to-date review of the extensive literature on forecast combinations, together with reference to available open-source software implementations. We discuss the potential and limitations of various methods and highlight how these ideas have developed over time. Some important issues concerning the utility of forecast combinations are also surveyed. Finally, we conclude with current research gaps and potential insights for future research.

We present a winning method of the IEEE DataPort Competition on Day-Ahead Electricity Demand Forecasting: Post-COVID Paradigm. The day-ahead load forecasting approach is based on online forecast combination of multiple point prediction models. It contains four steps: i) data cleaning and preprocessing, ii) a holiday adjustment procedure, iii) training of individual forecasting models, iv) forecast combination by smoothed Bernstein Online Aggregation (BOA). The approach is flexible and can quickly adopt to new energy system situations as they occurred during and after COVID-19 shutdowns. The pool of individual prediction models ranges from rather simple time series models to sophisticated models like generalized additive models (GAMs) and high-dimensional linear models estimated by lasso. They incorporate autoregressive, calendar and weather effects efficiently. All steps contain novel concepts that contribute to the excellent forecasting performance of the proposed method. This holds particularly for the holiday adjustment procedure and the fully adaptive smoothed BOA approach.

Forecast combination has been widely applied in the last few decades to improve forecast accuracy. In recent years, the idea of using time series features to construct forecast combination model has flourished in the forecasting area. Although this idea has been proved to be beneficial in several forecast competitions such as the M3 and M4 competitions, it may not be practical in many situations. For example, the task of selecting appropriate features to build forecasting models can be a big challenge for many researchers. Even if there is one acceptable way to define the features, existing features are estimated based on the historical patterns, which are doomed to change in the future, or infeasible in the case of limited historical data. In this work, we suggest a change of focus from the historical data to the produced forecasts to extract features. We calculate the diversity of a pool of models based on the corresponding forecasts as a decisive feature and use meta-learning to construct diversity-based forecast combination models. A rich set of time series are used to evaluate the performance of the proposed method. Experimental results show that our diversity-based forecast combination framework not only simplifies the modelling process but also achieves superior forecasting performance.

Many businesses and industries require accurate forecasts for weekly time series nowadays. The forecasting literature however does not currently provide easy-to-use, automatic, reproducible and accurate approaches dedicated to this task. We propose a forecasting method that can be used as a strong baseline in this domain, leveraging state-of-the-art forecasting techniques, forecast combination, and global modelling. Our approach uses four base forecasting models specifically suitable for forecasting weekly data: a global Recurrent Neural Network model, Theta, Trigonometric Box-Cox ARMA Trend Seasonal (TBATS), and Dynamic Harmonic Regression ARIMA (DHR-ARIMA). Those are then optimally combined using a lasso regression stacking approach. We evaluate the performance of our method against a set of state-of-the-art weekly forecasting models on six datasets. Across four evaluation metrics, we show that our method consistently outperforms the benchmark methods by a considerable margin with statistical significance. In particular, our model can produce the most accurate forecasts, in terms of mean sMAPE, for the M4 weekly dataset.

This paper studies the theoretical predictive properties of classes of forecast combination methods. The study is motivated by the recently developed Bayesian framework for synthesizing predictive densities: Bayesian predictive synthesis. A novel strategy based on continuous time stochastic processes is proposed and developed, where the combined predictive error processes are expressed as stochastic differential equations, evaluated using Ito's lemma. We show that a subclass of synthesis functions under Bayesian predictive synthesis, which we categorize as non-linear synthesis, entails an extra term that "corrects" the bias from misspecification and dependence in the predictive error process, effectively improving forecasts. Theoretical properties are examined and shown that this subclass improves the expected squared forecast error over any and all linear combination, averaging, and ensemble of forecasts, under mild conditions. We discuss the conditions for which this subclass outperforms others, and its implications for developing forecast combination methods. A finite sample simulation study is presented to illustrate our results.