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Time series often appear in an additive hierarchical structure. In such cases, time series on higher levels are the sums of their subordinate time series. This hierarchical structure places a natural constraint on forecasts. However,…

Methodology · Statistics 2025-03-20 Louis Steinmeister , Markus Pauly

We propose a novel approach to the problem of clustering hierarchically aggregated time-series data, which has remained an understudied problem though it has several commercial applications. We first group time series at each aggregated…

Machine Learning · Computer Science 2022-05-30 Xing Han , Tongzheng Ren , Jing Hu , Joydeep Ghosh , Nhat Ho

Multivariate time series forecasting with hierarchical structure is widely used in real-world applications, e.g., sales predictions for the geographical hierarchy formed by cities, states, and countries. The hierarchical time series (HTS)…

Machine Learning · Computer Science 2023-10-10 Fan Zhou , Chen Pan , Lintao Ma , Yu Liu , Shiyu Wang , James Zhang , Xinxin Zhu , Xuanwei Hu , Yunhua Hu , Yangfei Zheng , Lei Lei , Yun Hu

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…

Artificial Intelligence · Computer Science 2013-02-28 Ratnadip Adhikari , R. K. Agrawal

Combining forecast from different models has shown to perform better than single forecast in most time series. To improve the quality of forecast we can go for combining forecast. We study the effect of decomposing a series into multiple…

Applications · Statistics 2013-03-04 Manisha Gahirwal

In order to solve the problems such as difficult to extract effective features and low accuracy of sales volume prediction caused by complex relationships such as market sales volume in time series prediction, we proposed a time series…

Signal Processing · Electrical Eng. & Systems 2024-06-06 Jianyu Liu , Wei Chen , Yong Zhang , Zhenfeng Chen , Bin Wan , Jinwei Hu

Multiple seasonal patterns play a key role in time series forecasting, especially for business time series where seasonal effects are often dramatic. Previous approaches including Fourier decomposition, exponential smoothing, and seasonal…

Machine Learning · Statistics 2020-12-03 Hyunji Moon , Bomi Song , Hyeonseop Lee

Generating accurate and reliable sales forecasts is crucial in the E-commerce business. The current state-of-the-art techniques are typically univariate methods, which produce forecasts considering only the historical sales data of a single…

Machine Learning · Computer Science 2019-08-13 Kasun Bandara , Peibei Shi , Christoph Bergmeir , Hansika Hewamalage , Quoc Tran , Brian Seaman

Retail sales forecasting presents a significant challenge for large retailers such as Walmart and Amazon, due to the vast assortment of products, geographical location heterogeneity, seasonality, and external factors including weather,…

Machine Learning · Computer Science 2023-09-06 Tong Zhou

The features in many prediction models naturally take the form of a hierarchy. The lower levels represent individuals or events. These units group naturally into locations and intervals or other aggregates, often at multiple levels. Levels…

Applications · Statistics 2023-07-03 John Mark Agosta , Mario Inchiosa

Aggregation constraints, arising from geographical or sectoral division, frequently emerge in a large set of time series. Coherent forecasts of these constrained series are anticipated to conform to their hierarchical structure organized by…

Applications · Statistics 2026-02-27 Zhichao Wang , Shanshan Wang , Wei Cao , Fei Yang

Large collections of time series data are often organized into hierarchies with different levels of aggregation; examples include product and geographical groupings. Probabilistic coherent forecasting is tasked to produce forecasts…

The rapid proliferation of omnichannel retail strategies has fundamentally transformed store replenishment operations in uncertain supply chain environments. With retail stores increasingly acting as hybrid fulfillment centers, pooled…

Optimization and Control · Mathematics 2026-05-05 Abdüssamet Sökel

Many businesses and industries require accurate forecasts for weekly time series nowadays. However, the forecasting literature does not currently provide easy-to-use, automatic, reproducible and accurate approaches dedicated to this task.…

Machine Learning · Computer Science 2023-12-05 Rakshitha Godahewa , Christoph Bergmeir , Geoffrey I. Webb , Pablo Montero-Manso

Standard LSTM(Long Short-Term Memory) neural networks provide accurate predictions for sales data in the retail industry, but require a lot of computing power. It can be challenging especially for mid to small retail industries. This paper…

Machine Learning · Computer Science 2026-02-19 Ravi Teja Pagidoju

Ads demand forecasting for Walmart's ad products plays a critical role in enabling effective resource planning, allocation, and management of ads performance. In this paper, we introduce a comprehensive demand forecasting system that…

Machine Learning · Computer Science 2024-12-20 Zhengchao Yang , Mithun Ghosh , Anish Saha , Dong Xu , Konstantin Shmakov , Kuang-chih Lee

This paper focuses on forecasting hierarchical time-series data, where each higher-level observation equals the sum of its corresponding lower-level time series. In such contexts, the forecast values should be coherent, meaning that the…

Machine Learning · Computer Science 2026-02-06 Shuhei Aikawa , Aru Suzuki , Kei Yoshitake , Kanata Teshigawara , Akira Iwabuchi , Ken Kobayashi , Kazuhide Nakata

This work evaluates the effectiveness of spatiotemporal Graph Neural Networks (GNNs) for multi-store retail sales forecasting and compares their performance against ARIMA, LSTM, and XGBoost baselines. Using weekly sales data from 45 Walmart…

Machine Learning · Computer Science 2025-11-25 Manish Singh , Arpita Dayama

Accurate prediction of financial time series is a key concern for market economy makers and investors. The article selects online store sales and Australian beer sales as representatives of non-stationary, trending, and seasonal financial…

Signal Processing · Electrical Eng. & Systems 2024-06-10 Wei Chen , Yuanyuan Yang , Jianyu Liu

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…

Applications · Statistics 2021-12-17 Xixi Li , Fotios Petropoulos , Yanfei Kang
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