This paper introduces a novel meta-learning algorithm for time series forecast model performance prediction. We model the forecast error as a function of time series features calculated from historical time series with an efficient Bayesian multivariate surface regression approach. The minimum predicted forecast error is then used to identify an individual model or a combination of models to produce the final forecasts. It is well known that the performance of most meta-learning models depends on the representativeness of the reference dataset used for training. In such circumstances, we augment the reference dataset with a feature-based time series simulation approach, namely GRATIS, to generate a rich and representative time series collection. The proposed framework is tested using the M4 competition data and is compared against commonly used forecasting approaches. Our approach provides comparable performance to other model selection and combination approaches but at a lower computational cost and a higher degree of interpretability, which is important for supporting decisions. We also provide useful insights regarding which forecasting models are expected to work better for particular types of time series, the intrinsic mechanisms of the meta-learners, and how the forecasting performance is affected by various factors.

Hierarchical forecasting with intermittent time series is a challenge in both research and empirical studies. Extensive research focuses on improving the accuracy of each hierarchy, especially the intermittent time series at bottom levels. Then, hierarchical reconciliation can be used to improve the overall performance further. In this paper, we present a hierarchical-forecasting-with-alignment approach that treats the bottom-level forecasts as mutable to ensure higher forecasting accuracy on the upper levels of the hierarchy. We employ a pure deep learning forecasting approach, N-BEATS, for continuous time series at the top levels, and a widely used tree-based algorithm, LightGBM, for intermittent time series at the bottom level. The hierarchical-forecasting-with-alignment approach is a simple yet effective variant of the bottom-up method, accounting for biases that are difficult to observe at the bottom level. It allows suboptimal forecasts at the lower level to retain a higher overall performance. The approach in this empirical study was developed by the first author during the M5 Accuracy competition, ranking second place. The method is also business orientated and can be used to facilitate strategic business planning.

The semi-open character with high passenger flow in Metro Rail Transport Stations (MRTS) makes safety management of human-electromechanical interaction escalator systems more complex. Safety management should not consider only single failures, but also the complex interactions in the system. This study applies task driven behavior theory and system theory to reveal a generic framework of the MRTS escalator accident mechanism and uses Lasso-Logistic Regression (LLR) for escalator injury prediction. Escalator accidents in the Beijing MRTS are used as a case study to estimate the applicability of the methodologies. The main results affirm that the application of System-Theoretical Process Analysis (STPA) and Task Driven Accident Process Analysis (TDAPA) to the generic escalator accident mechanism reveals non-failure state task driven passenger behaviors and constraints on safety that are not addressed in previous studies. The results also confirm that LLR is able to predict escalator accidents where there is a relatively large number of variables with limited observations. Additionally, increasing the amount of data improves the prediction accuracy for all three types of injuries in the case study, suggesting the LLR model has good extrapolation ability. The results can be applied in MRTS as instruments for both escalator accident investigation and accident prevention.

Forecast combinations have been widely applied in the last few decades to improve forecasting. Estimating optimal weights that can outperform simple averages is not always an easy task. In recent years, the idea of using time series features for forecast combinations has flourished. Although this idea has been proved to be beneficial in several forecasting competitions, it may not be practical in many situations. For example, the task of selecting appropriate features to build forecasting models is often challenging. Even if there was an acceptable way to define the features, existing features are estimated based on the historical patterns, which are likely to change in the future. Other times, the estimation of the features is infeasible due to limited historical data. In this work, we suggest a change of focus from the historical data to the produced forecasts to extract features. We use out-of-sample forecasts to obtain weights for forecast combinations by amplifying the diversity of the pool of methods being combined. A rich set of time series is used to evaluate the performance of the proposed method. Experimental results show that our diversity-based forecast combination framework not only simplifies the modeling process but also achieves superior forecasting performance in terms of both point forecasts and prediction intervals. The value of our proposition lies on its simplicity, transparency, and computational efficiency, elements that are important from both an optimization and a decision analysis perspective.

Forecasting has always been at the forefront of decision making and planning. The uncertainty that surrounds the future is both exciting and challenging, with individuals and organisations seeking to minimise risks and maximise utilities. The large number of forecasting applications calls for a diverse set of forecasting methods to tackle real-life challenges. This article provides a non-systematic review of the theory and the practice of forecasting. We provide an overview of a wide range of theoretical, state-of-the-art models, methods, principles, and approaches to prepare, produce, organise, and evaluate forecasts. We then demonstrate how such theoretical concepts are applied in a variety of real-life contexts. We do not claim that this review is an exhaustive list of methods and applications. However, we wish that our encyclopedic presentation will offer a point of reference for the rich work that has been undertaken over the last decades, with some key insights for the future of forecasting theory and practice. Given its encyclopedic nature, the intended mode of reading is non-linear. We offer cross-references to allow the readers to navigate through the various topics. We complement the theoretical concepts and applications covered by large lists of free or open-source software implementations and publicly-available databases.

Quantile regression is a method of fundamental importance. How to efficiently conduct quantile regression for a large dataset on a distributed system is of great importance. We show that the popularly used one-shot estimation is statistically inefficient if data are not randomly distributed across different workers. To fix the problem, a novel one-step estimation method is developed with the following nice properties. First, the algorithm is communication efficient. That is the communication cost demanded is practically acceptable. Second, the resulting estimator is statistically efficient. That is its asymptotic covariance is the same as that of the global estimator. Third, the estimator is robust against data distribution. That is its consistency is guaranteed even if data are not randomly distributed across different workers. Numerical experiments are provided to corroborate our findings. A real example is also presented for illustration.

Forecasting is an indispensable element of operational research (OR) and an important aid to planning. The accurate estimation of the forecast uncertainty facilitates several operations management activities, predominantly in supporting decisions in inventory and supply chain management and effectively setting safety stocks. In this paper, we introduce a feature-based framework, which links the relationship between time series features and the interval forecasting performance into providing reliable interval forecasts. We propose an optimal threshold ratio searching algorithm and a new weight determination mechanism for selecting an appropriate subset of models and assigning combination weights for each time series tailored to the observed features. We evaluate our approach using a large set of time series from the M4 competition. Our experiments show that our approach significantly outperforms a wide range of benchmark models, both in terms of point forecasts as well as prediction intervals.