arXiv subjects

Yanfei Kang

Publications and source records attributed to Yanfei Kang.

At least 19 recordsLinked to original sources

arXiv2026

REGAIN: REconciliation GAIN-driven Auxiliary Direction Learning

Forecast reconciliation usually starts from a fixed measurement system and asks how forecasts should be projected onto a coherent space. We ask a different question: which additional linear measurements should be forecast and included in the reconciliation system? We propose REGAIN, a reconciliation-gain framework that learns normalized auxiliary directions, forecasts the induced series with a frozen forecasting oracle, and selects directions by their target-weighted loss reduction after augmented generalized least-squares reconciliation. Unlike variance-based components or predictability-based auxiliary selection, REGAIN optimizes the downstream effect of an auxiliary measurement on the final reconciled forecasts. We provide a statistical characterization showing that useful auxiliary directions must provide complementary information about unresolved target uncertainty, rather than merely being easy to forecast. The analysis also clarifies the covariance-risk reduction mechanism, the role of bias changes in realized quadratic risk, and the stability of estimated gain signals. A stagewise learning algorithm with held-out gain screening is developed, together with an optional joint refinement step. Experiments on Beijing PM2.5 and Australian Tourism data show that gain-selected measurements can improve both ordinary multivariate and hierarchical forecasts, especially when they reveal residual uncertainty not captured by the original measurement system.

stat.ML↗

arXiv2026

Multi-objective probabilistic forecast combination for inventory demand

Probabilistic forecasts are essential for inventory management, where decisions depend on the full distribution of future demand. While probabilistic forecast combination is widely used to improve statistical accuracy, most existing approaches optimize statistical loss alone and overlook operational objectives. However, in inventory settings, higher forecast accuracy does not necessarily translate into better decision performance, especially under nonlinear cost structures and multiple, potentially conflicting, decision targets. To address this gap, we propose a multi-objective probabilistic forecast combination framework that simultaneously considers forecast accuracy and inventory decision performance. The framework formulates forecast combination as a multi-objective optimization problem and derives a set of Pareto-optimal combinations, enabling explicit trade-offs between forecasting and operational goals. Empirical studies using Walmart retail data and Royal Air Force spare parts data demonstrate that the proposed approach achieves more balanced and robust performance than individual models, simple averaging, and single-objective optimization. Our results provide a practical and flexible framework for aligning probabilistic forecasting with inventory decision-making.

stat.AP↗

arXiv2025

Bayesian Forecast Combination with Predictive Priors via Particle Filtering

We propose a Bayesian forecast combination framework that, for the first time, embeds forward-looking signals, formulated as predictive priors, directly into the time-varying weight-updating process. This approach enables weights to adapt using both historical forecast performance and anticipated future model behavior. We implement the framework with model diversity as the forward-looking signal, yielding the diversity-driven time-varying weights (DTVW) method. Compared with the standard time-varying weights (TVW) approach, DTVW embeds diversity-driven predictive priors that penalize redundancy and encourage informative contributions across constituent models. Simulation experiments, covering both a simple complete model set and a complex misspecified environment, show that DTVW improves forecast accuracy by dynamically focusing on well-performing models. Empirical applications to multi-step-ahead oil price forecasts and bivariate forecasts of U.S. inflation and GDP growth confirm its superiority over benchmarks including Equal weighting, Bayesian Model Averaging, and standard TVW. Beyond accuracy gains, diversity-based predictive priors provide diagnostic insights into model incompleteness and forecast uncertainty, making DTVW both more adaptive and more informative than existing Bayesian combination methods.

stat.ME↗

arXiv2023

Probabilistic Forecast Reconciliation with Kullback-Leibler Divergence Regularization

As the popularity of hierarchical point forecast reconciliation methods increases, there is a growing interest in probabilistic forecast reconciliation. Many studies have utilized machine learning or deep learning techniques to implement probabilistic forecasting reconciliation and have made notable progress. However, these methods treat the reconciliation step as a fixed and hard post-processing step, leading to a trade-off between accuracy and coherency. In this paper, we propose a new approach for probabilistic forecast reconciliation. Unlike existing approaches, our proposed approach fuses the prediction step and reconciliation step into a deep learning framework, making the reconciliation step more flexible and soft by introducing the Kullback-Leibler divergence regularization term into the loss function. The approach is evaluated using three hierarchical time series datasets, which shows the advantages of our approach over other probabilistic forecast reconciliation methods.

cs.AI↗

arXiv2023

Infinite forecast combinations based on Dirichlet process

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.

cs.LG↗

arXiv2023

Forecasting large collections of time series: feature-based methods

In economics and many other forecasting domains, the real world problems are too complex for a single model that assumes a specific data generation process. The forecasting performance of different methods changes depending on the nature of the time series. When forecasting large collections of time series, two lines of approaches have been developed using time series features, namely feature-based model selection and feature-based model combination. This chapter discusses the state-of-the-art feature-based methods, with reference to open-source software implementations.

cs.LG↗

arXiv2023

Discrete forecast reconciliation

This paper presents a formal framework and proposes algorithms to extend forecast reconciliation to discrete-valued data to extend forecast reconciliation to discrete-valued data, including low counts. A novel method is introduced based on recasting the optimisation of scoring rules as an assignment problem, which is solved using quadratic programming. The proposed framework produces coherent joint probabilistic forecasts for count hierarchical time series. Two discrete reconciliation algorithms are also proposed and compared against generalisations of the top-down and bottom-up approaches for count data. Two simulation experiments and two empirical examples are conducted to validate that the proposed reconciliation algorithms improve forecast accuracy. The empirical applications are forecasting criminal offences in Washington D.C. and product unit sales in the M5 dataset. Compared to benchmarks, the proposed framework shows superior performance in both simulations and empirical studies.

stat.ME↗

arXiv2023

Combining Probabilistic Forecasts of Intermittent Demand

In recent decades, new methods and approaches have been developed for forecasting intermittent demand series. However, the majority of research has focused on point forecasting, with little exploration into probabilistic intermittent demand forecasting. This is despite the fact that probabilistic forecasting is crucial for effective decision-making under uncertainty and inventory management. Additionally, most literature on this topic has focused solely on forecasting performance and has overlooked the inventory implications, which are directly relevant to intermittent demand. To address these gaps, this study aims to construct probabilistic forecasting combinations for intermittent demand while considering both forecasting accuracy and inventory control utility in obtaining combinations and evaluating forecasts. Our empirical findings demonstrate that combinations perform better than individual approaches for forecasting intermittent demand, but there is a trade-off between forecasting and inventory performance.

stat.AP↗

arXiv2022

Predict+Optimize Problem in Renewable Energy Scheduling

Predict+Optimize frameworks integrate forecasting and optimization to address real-world challenges such as renewable energy scheduling, where variability and uncertainty are critical factors. This paper benchmarks solutions from the IEEE-CIS Technical Challenge on Predict+Optimize for Renewable Energy Scheduling, focusing on forecasting renewable production and demand and optimizing energy cost. The competition attracted 49 participants in total. The top-ranked method employed stochastic optimization using LightGBM ensembles, and achieved at least a 2% reduction in energy costs compared to deterministic approaches, demonstrating that the most accurate point forecast does not necessarily guarantee the best performance in downstream optimization. The published data and problem setting establish a benchmark for further research into integrated forecasting-optimization methods for energy systems, highlighting the importance of considering forecast uncertainty in optimization models to achieve cost-effective and reliable energy management. The novelty of this work lies in its comprehensive evaluation of Predict+Optimize methodologies applied to a real-world renewable energy scheduling problem, providing insights into the scalability, generalizability, and effectiveness of the proposed solutions. Potential applications extend beyond energy systems to any domain requiring integrated forecasting and optimization, such as supply chain management, transportation planning, and financial portfolio optimization.

cs.AI↗

arXiv2022

Forecast combinations: an over 50-year review

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.

stat.ME↗

arXiv2022

Feature-based intermittent demand forecast combinations: bias, accuracy and inventory implications

Intermittent demand forecasting is a ubiquitous and challenging problem in production systems and supply chain management. In recent years, there has been a growing focus on developing forecasting approaches for intermittent demand from academic and practical perspectives. However, limited attention has been given to forecast combination methods, which have achieved competitive performance in forecasting fast-moving time series. The current study aims to examine the empirical outcomes of some existing forecast combination methods and propose a generalized feature-based framework for intermittent demand forecasting. The proposed framework has been shown to improve the accuracy of point and quantile forecasts based on two real data sets. Further, some analysis of features, forecasting pools and computational efficiency is also provided. The findings indicate the intelligibility and flexibility of the proposed approach in intermittent demand forecasting and offer insights regarding inventory decisions.

stat.AP↗

arXiv2022

Another look at forecast trimming for combinations: robustness, accuracy and diversity

Forecast combination is widely recognized as a preferred strategy over forecast selection due to its ability to mitigate the uncertainty associated with identifying a single "best" forecast. Nonetheless, sophisticated combinations are often empirically dominated by simple averaging, which is commonly attributed to the weight estimation error. The issue becomes more problematic when dealing with a forecast pool containing a large number of individual forecasts. In this paper, we propose a new forecast trimming algorithm to identify an optimal subset from the original forecast pool for forecast combination tasks. In contrast to existing approaches, our proposed algorithm simultaneously takes into account the robustness, accuracy and diversity issues of the forecast pool, rather than isolating each one of these issues. We also develop five forecast trimming algorithms as benchmarks, including one trimming-free algorithm and several trimming algorithms that isolate each one of the three key issues. Experimental results show that our algorithm achieves superior forecasting performance in general in terms of both point forecasts and prediction intervals. Nevertheless, we argue that diversity does not always have to be addressed in forecast trimming. Based on the results, we offer some practical guidelines on the selection of forecast trimming algorithms for a target series.

stat.ME↗

arXiv2022

Bayesian forecast combination using time-varying features

In this work, we propose a novel framework for density forecast combination by constructing time-varying weights based on time series features, which is called Feature-based Bayesian Forecasting Model Averaging (FEBAMA). Our framework estimates weights in the forecast combination via Bayesian log predictive scores, in which the optimal forecasting combination is determined by time series features from historical information. In particular, we use an automatic Bayesian variable selection method to add weight to the importance of different features. To this end, our approach has better interpretability compared to other black-box forecasting combination schemes. We apply our framework to stock market data and M3 competition data. Based on our structure, a simple maximum-a-posteriori scheme outperforms benchmark methods, and Bayesian variable selection can further enhance the accuracy for both point and density forecasts.

econ.EM↗

arXiv2022

Optimal reconciliation with immutable forecasts

The practical importance of coherent forecasts in hierarchical forecasting has inspired many studies on forecast reconciliation. Under this approach, so-called base forecasts are produced for every series in the hierarchy and are subsequently adjusted to be coherent in a second reconciliation step. Reconciliation methods have been shown to improve forecast accuracy, but will, in general, adjust the base forecast of every series. However, in an operational context, it is sometimes necessary or beneficial to keep forecasts of some variables unchanged after forecast reconciliation. In this paper, we formulate reconciliation methodology that keeps forecasts of a pre-specified subset of variables unchanged or "immutable". In contrast to existing approaches, these immutable forecasts need not all come from the same level of a hierarchy, and our method can also be applied to grouped hierarchies. We prove that our approach preserves unbiasedness in base forecasts. Our method can also account for correlations between base forecasting errors and ensure non-negativity of forecasts. We also perform empirical experiments, including an application to sales of a large scale online retailer, to assess the impacts of our proposed methodology.

stat.ME↗

arXiv2022

Forecasting: theory and practice

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.

stat.AP↗

arXiv2021

Improving forecasting by subsampling seasonal time series

Time series forecasting plays an increasingly important role in modern business decisions. In today's data-rich environment, people often aim to choose the optimal forecasting model for their data. However, identifying the optimal model requires professional knowledge and experience, making accurate forecasting a challenging task. To mitigate the importance of model selection, we propose a simple and reliable algorithm to improve the forecasting performance. Specifically, we construct multiple time series with different sub-seasons from the original time series. These derived series highlight different sub-seasonal patterns of the original series, making it possible for the forecasting methods to capture diverse patterns and components of the data. Subsequently, we produce forecasts for these multiple series separately with classical statistical models (ETS or ARIMA). Finally, the forecasts are combined. We evaluate our approach on widely-used forecasting competition data sets (M1, M3, and M4) in terms of both point forecasts and prediction intervals. We observe performance improvements compared with the benchmarks. Our approach is particularly suitable and robust for the data with higher frequency. To demonstrate the practical value of our proposition, we showcase the performance improvements from our approach on hourly load data that exhibit multiple seasonal patterns.

stat.AP↗

arXiv2021

Exploring the social influence of Kaggle virtual community on the M5 competition

One of the most significant differences of M5 over previous forecasting competitions is that it was held on Kaggle, an online platform of data scientists and machine learning practitioners. Kaggle provides a gathering place, or virtual community, for web users who are interested in the M5 competition. Users can share code, models, features, loss functions, etc. through online notebooks and discussion forums. This paper aims to study the social influence of virtual community on user behaviors in the M5 competition. We first research the content of the M5 virtual community by topic modeling and trend analysis. Further, we perform social media analysis to identify the potential relationship network of the virtual community. We study the roles and characteristics of some key participants that promote the diffusion of information within the M5 virtual community. Overall, this study provides in-depth insights into the mechanism of the virtual community's influence on the participants and has potential implications for future online competitions.

cs.SI↗

arXiv2021

Forecast with Forecasts: Diversity Matters

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 combination 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 modelling 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 optimisation and a decision analysis perspective.

stat.ME↗