[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-125204-en":3,"doc-seo-125204-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},125204,1099514067415,"Rowan","https://ap-avatar.wpscdn.com/avatar/100002539d78ffe74a7?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779092875211072502",8,"Research & Report","Linear and machine learning cross-temporal forecast reconciliation - An empirical investigation","Forecast reconciliation is a post-forecasting process that enforces coherence for linear-constrained time series by aligning predictions across different aggregation levels. This thesis investigates a cross-temporal framework and compares linear and machine learning-based reconciliation solutions using two empirical applications: Citi Bike rental demand and Energy Load. The datasets share temporal structure but differ in cross-sectional hierarchy and industry context. The study evaluates covariance matrix choices, residual handling, and non-negativity consistency. Results show linear methods outperform ML approaches; heuristic and optimal linear reconciliation achieve the highest accuracy, while Random Forest is strongest among ML methods.","University of Padova  \nDepartment of mathematics Tullio-Levi Civita Master Thesis in Data Science  \nLinear and machine learning cross-temporal forecast reconciliation: An empirical investigation  \nSupervisor Master Candidate  \nProfessor Luisa Bisaglia Roya Ghamari  \nUniversity of Padova 2071969  \nCo-supervisor  \nDoctor Daniele Girolimetto University of Padova  \nAcademic Year  \n2024-2025  \nii  \nI dedicate this work to my parents and my brother, who have always supported me. I also want to dedicate this thesis to my cousin, whose life was cut short at a young age. The pain of losing her will always remain with us, and she will always be remembered with love.  \niv  \nAbstract  \nForecast reconciliation is a post forecasting process that ensures coherence when dealing with linear constraints time series, aligning predictions at different levels of aggregation. Exploring the cross-temporal framework, this thesis compares different linear and machine learning-based solutions with two empirical applications: Citi Bike rental demand and Energy Load. While both datasets share the same temporal structure, they differ in cross-sectional hierarchy and industry context, allowing for a broader evaluation of reconciliation methods.  \nKey concepts in this study include evaluating different reconciliation strategies by exploring various covariance matrix structures, refining residual handling in linear and machine learningbased models, and ensuring consistency in non-negativity constraints across all reconciliation methods. The results indicate that, in contrast to prior findings, linear reconciliation methods consistently outperformed ML-based approaches. Among the linear models, heuristic and optimal linear reconciliation approaches demonstrated the highest forecast accuracy. On the other hand, Random Forest remained the strongest ML-based reconciliation method.  \nSensitivity analyses revealed that including a wide range of temporal aggregation levels generally improves accuracy, reinforcing the value of comprehensive reconciliation structures. The choice between compact and complete feature matrices had a notable impact on ML reconciliation performance, with its effects varying across hierarchical levels. These findings highlight the importance of methodological choices in reconciliation and their influence on forecast accuracy.  \nFuture work could explore reconciliation using neural network-based ML algorithms, automated feature selection techniques, and online learning approaches for dynamic model updatesand improved computational efficiency.  \nvi  \nContents  \nAbstract v  \nList of figures ix  \nList of tables xi  \nListing of acronyms xiii  \n1 Introduction 1  \n1.1 Time Series, Forecasting, and Hierarchical Structure ............. 1  \n1.2 Forecast Reconciliation Approaches ...................... 2  \n1.3 Context of the Data .............................. 3  \n1.4 Outlines of the Thesis ............................. 4  \n2 Objectives 7  \n3 Data 9  \n3.1 Bicycle sharing platform data ......................... 9  \n3.2 Energy load data of Italy ............................ 15  \n4 Methodology 23  \n4.1 Forecast set-up ................................. 23  \n4.2 Traditional Time Series Models for Base Forecasting ............. 24  \n4.3 Machine Learning Methods for Forecast Reconciliation ............ 25  \n4.4 Linear Reconciliation Benchmarks for Cross-Temporal Hierarchies ...... 27  \n4.4.1 Reconciliation forecast methods ................... 27  \n4.4.2 Covariance matrices   28  \n4.5 Evaluation Metrics ............................... 29  \n4.5.1 Weighted Absolute Percentage Error ................. 29  \n4.5.2 Mean Absolute Scaled Error ..................... 30  \n5 Results and discussion 33  \n5.1 Results for bicycle sharing data ........................ 33  \n5.1.1 Overall forecast performance ..................... 33  \n5.1.2 Sensitivity to Feature Matrices .................... 34  \n5.1.3 Sensitivity to Temporal Aggregation Orders ............. 41  \n5.2 Results","cbCaigmGX3QkudDe","https://ap.wps.com/l/cbCaigmGX3QkudDe","pdf",4437172,1,112,"English","en",105,"# Introduction\n## Time Series, Forecasting, and Hierarchical Structure\n## Forecast Reconciliation Approaches\n## Context of the Data\n## Outlines of the Thesis\n# Objectives\n# Data\n## Bicycle sharing platform data\n## Energy load data of Italy\n# Methodology\n## Forecast set-up\n## Traditional Time Series Models for Base Forecasting\n## Machine Learning Methods for Forecast Reconciliation\n## Linear Reconciliation Benchmarks for Cross-Temporal Hierarchies\n## Evaluation Metrics\n# Results and discussion\n## Results for bicycle sharing data\n## Results for energy load data\n# Conclusion\n## Addressing the Study Objectives\n## Summary of Results and Dataset Comparisons\n## Limitations and Future Works","[{\"question\":\"What is forecast reconciliation in this thesis?\",\"answer\":\"Forecast reconciliation is a post-forecasting step that ensures coherent predictions when time series are subject to linear constraints. It aligns forecasts across different levels of aggregation.\"},{\"question\":\"Which datasets are used to evaluate reconciliation methods?\",\"answer\":\"The thesis evaluates methods using Citi Bike rental demand and Italy Energy Load. Both share the same temporal structure but differ in cross-sectional hierarchy and application context.\"},{\"question\":\"How do linear reconciliation methods compare with machine learning approaches?\",\"answer\":\"The results indicate linear reconciliation methods consistently outperform ML-based approaches. Among linear models, heuristic and optimal approaches show the highest accuracy, while Random Forest is the strongest ML method.\"}]","Linear and machine learning cross-temporal forecast reconciliation - An empirical investigation | PDF",1785897388,282,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"linear-and-machine-learning-cross-temporal-forecast-reconciliation-an-empirical-investigation","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/linear-and-machine-learning-cross-temporal-forecast-reconciliation-an-empirical-investigation/125204/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-05",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What is forecast reconciliation in this thesis?","Question",{"text":75,"@type":76},"Forecast reconciliation is a post-forecasting step that ensures coherent predictions when time series are subject to linear constraints. It aligns forecasts across different levels of aggregation.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"Which datasets are used to evaluate reconciliation methods?",{"text":80,"@type":76},"The thesis evaluates methods using Citi Bike rental demand and Italy Energy Load. Both share the same temporal structure but differ in cross-sectional hierarchy and application context.",{"name":82,"@type":73,"acceptedAnswer":83},"How do linear reconciliation methods compare with machine learning approaches?",{"text":84,"@type":76},"The results indicate linear reconciliation methods consistently outperform ML-based approaches. 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