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The self-similar analysis of time series is generalized by introducing the notion of scenario probabilities. This makes it possible to give a complete statistical description for the forecast spectrum by defining the average forecast as a…

凝聚态物理 · 物理学 2009-10-31 V. I. Yukalov , S. Gluzman

The forecasting combination puzzle is a well-known phenomenon in forecasting literature, stressing the challenge of outperforming the simple average when aggregating forecasts from diverse methods. This study proposes a Reinforcement…

计量经济学 · 经济学 2025-08-29 Marcelo C. Medeiros , Jeronymo M. Pinro

Forecast reconciliation is considered an effective method to achieve coherence (within a forecast hierarchy) and to improve forecast quality. However, the value of reconciled forecasts in downstream decision-making tasks has been mostly…

机器学习 · 统计学 2025-12-02 Honglin Wen , Pierre Pinson

In minimum trace (MinT) forecast reconciliation, the covariance matrix of the base forecasts errors plays a crucial role. Typically, this matrix is estimated and then treated as known. This can lead to underestimation of the variance of the…

统计方法学 · 统计学 2026-05-11 Chiara Carrara , Dario Azzimonti , Giorgio Corani , Lorenzo Zambon

New methods are proposed for adjusting probabilistic forecasts to ensure coherence with the aggregation constraints inherent in temporal hierarchies. The different approaches nested within this framework include methods that exploit…

统计方法学 · 统计学 2020-08-18 Jooyoung Jeon , Anastasios Panagiotelis , Fotios Petropoulos

Calibration is a pivotal aspect in predictive modeling, as it ensures that the predictions closely correspond with what we observe empirically. The contemporary calibration framework, however, is predominantly focused on prediction models…

统计方法学 · 统计学 2023-09-18 Bavo De Cock Campo

When forecasting time series with a hierarchical structure, the existing state of the art is to forecast each time series independently, and, in a post-treatment step, to reconcile the time series in a way that respects the hierarchy…

机器学习 · 统计学 2019-06-26 Konstantin Mishchenko , Mallory Montgomery , Federico Vaggi

Time series forecasting presents unique challenges that limit the effectiveness of traditional machine learning algorithms. To address these limitations, various approaches have incorporated linear constraints into learning algorithms, such…

机器学习 · 统计学 2025-02-18 Nathan Doumèche , Francis Bach , Éloi Bedek , Gérard Biau , Claire Boyer , Yannig Goude

Forecast reconciliation has become key to improving the accuracy and coherence of forecasts for linearly constrained multiple time series, such as hierarchical and grouped series. Yet, comprehensive software that jointly covers…

统计计算 · 统计学 2026-05-01 Daniele Girolimetto , Jeroen Rombouts , Ines Wilms , Yangzhuoran Fin Yang

Although contrastive and other representation-learning methods have long been explored in vision and NLP, their adoption in modern time series forecasters remains limited. We believe they hold strong promise for this domain. To unlock this…

机器学习 · 计算机科学 2026-03-26 Yifan Hu , Jie Yang , Tian Zhou , Peiyuan Liu , Yujin Tang , Rong Jin , Liang Sun

Forecast combination -- the aggregation of individual forecasts from multiple experts or models -- is a proven approach to economic forecasting. To date, research on economic forecasting has concentrated on local combination methods, which…

计量经济学 · 经济学 2024-03-12 Ryan Thompson , Yilin Qian , Andrey L. Vasnev

Conformal Prediction is a framework that produces prediction intervals based on the output from a machine learning algorithm. In this paper we explore the case when training data is made up of multiple parts available in different sources…

机器学习 · 统计学 2019-08-16 Ola Spjuth , Robin Carrión Brännström , Lars Carlsson , Niharika Gauraha

It is often reported in forecast combination literature that a simple average of candidate forecasts is more robust than sophisticated combining methods. This phenomenon is usually referred to as the "forecast combination puzzle". Motivated…

统计方法学 · 统计学 2015-05-05 Wei Qian , Craig A. Rolling , Gang Cheng , Yuhong Yang

Conformal predictive systems are sets of predictive distributions with theoretical out-of-sample calibration guarantees. The calibration guarantees are typically that the set of predictions contains a forecast distribution whose prediction…

统计方法学 · 统计学 2025-11-03 Sam Allen , Enrico Pescara , Johanna Ziegel

Machine learning-based weather forecasting models now surpass state-of-the-art numerical weather prediction systems, but training and operating these models at high spatial resolution remains computationally expensive. We present a modular…

机器学习 · 计算机科学 2026-04-02 Aymeric Delefosse , Anastase Charantonis , Dominique Béréziat

Conformal prediction is a powerful post-hoc framework for uncertainty quantification that provides distribution-free coverage guarantees. However, these guarantees crucially rely on the assumption of exchangeability. This assumption is…

统计方法学 · 统计学 2025-11-18 M. Stocker , W. Małgorzewicz , M. Fontana , S. Ben Taieb

The standard implementation of the conjugate gradient algorithm suffers from communication bottlenecks on parallel architectures, due primarily to the two global reductions required every iteration. In this paper, we study conjugate…

数值分析 · 计算机科学 2021-04-20 Tyler Chen , Erin C. Carson

Improvement of time series forecasting accuracy through combining multiple models is an important as well as a dynamic area of research. As a result, various forecasts combination methods have been developed in literature. However, most of…

人工智能 · 计算机科学 2013-02-28 Ratnadip Adhikari , R. K. Agrawal

Chaotic dynamical systems exhibit strong sensitivity to initial conditions and often contain unresolved multiscale processes, making deterministic forecasting fundamentally limited. Generative models offer an appealing alternative by…

机器学习 · 计算机科学 2026-01-01 Patrick Wyrod , Ashesh Chattopadhyay , Daniele Venturi

Time series forecasting traditionally relies on unimodal numerical inputs, which often struggle to capture high-level semantic patterns due to their dense and unstructured nature. While recent approaches have explored representing time…

机器学习 · 计算机科学 2025-07-02 Sixun Dong , Wei Fan , Teresa Wu , Yanjie Fu