{"id":"https://openalex.org/W4413904839","doi":"https://doi.org/10.1016/j.ipm.2025.104358","title":"Learning hierarchical time\u2013frequency representation for long-term time series forecasting","display_name":"Learning hierarchical time\u2013frequency representation for long-term time series forecasting","publication_year":2025,"publication_date":"2025-09-01","ids":{"openalex":"https://openalex.org/W4413904839","doi":"https://doi.org/10.1016/j.ipm.2025.104358"},"language":"en","primary_location":{"id":"doi:10.1016/j.ipm.2025.104358","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.ipm.2025.104358","pdf_url":null,"source":{"id":"https://openalex.org/S174847851","display_name":"Information Processing & Management","issn_l":"0306-4573","issn":["0306-4573","1873-5371"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Information Processing &amp; Management","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1016/j.ipm.2025.104358","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064109559","display_name":"Zhongju Wang","orcid":"https://orcid.org/0000-0001-5124-6519"},"institutions":[{"id":"https://openalex.org/I188329596","display_name":"University of Canberra","ror":"https://ror.org/04s1nv328","country_code":"AU","type":"education","lineage":["https://openalex.org/I188329596"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Zhongju Wang","raw_affiliation_strings":["School of Systems and Computing, University of New South Wales Canberra, 2600, ACT, Australia"],"raw_orcid":"https://orcid.org/0000-0001-5124-6519","affiliations":[{"raw_affiliation_string":"School of Systems and Computing, University of New South Wales Canberra, 2600, ACT, Australia","institution_ids":["https://openalex.org/I188329596"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100586111","display_name":"Zhenhong Sun","orcid":null},"institutions":[{"id":"https://openalex.org/I118347636","display_name":"Australian National University","ror":"https://ror.org/019wvm592","country_code":"AU","type":"education","lineage":["https://openalex.org/I118347636"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Zhenhong Sun","raw_affiliation_strings":["Australian National University, Canberra, 0200, ACT, Australia"],"raw_orcid":"https://orcid.org/0009-0000-5135-0658","affiliations":[{"raw_affiliation_string":"Australian National University, Canberra, 0200, ACT, Australia","institution_ids":["https://openalex.org/I118347636"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045777220","display_name":"Yatao Bian","orcid":"https://orcid.org/0000-0002-2368-4084"},"institutions":[{"id":"https://openalex.org/I2250653659","display_name":"Tencent (China)","ror":"https://ror.org/00hhjss72","country_code":"CN","type":"company","lineage":["https://openalex.org/I2250653659"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yatao Bian","raw_affiliation_strings":["Tencent AI Lab, China"],"raw_orcid":"https://orcid.org/0000-0002-2368-4084","affiliations":[{"raw_affiliation_string":"Tencent AI Lab, China","institution_ids":["https://openalex.org/I2250653659"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061835916","display_name":"Huadong Mo","orcid":"https://orcid.org/0000-0002-7782-2884"},"institutions":[{"id":"https://openalex.org/I188329596","display_name":"University of Canberra","ror":"https://ror.org/04s1nv328","country_code":"AU","type":"education","lineage":["https://openalex.org/I188329596"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Huadong Mo","raw_affiliation_strings":["School of Systems and Computing, University of New South Wales Canberra, 2600, ACT, Australia"],"raw_orcid":"https://orcid.org/0000-0002-7782-2884","affiliations":[{"raw_affiliation_string":"School of Systems and Computing, University of New South Wales Canberra, 2600, ACT, Australia","institution_ids":["https://openalex.org/I188329596"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000582423","display_name":"Daoyi Dong","orcid":"https://orcid.org/0000-0002-7425-3559"},"institutions":[{"id":"https://openalex.org/I118347636","display_name":"Australian National University","ror":"https://ror.org/019wvm592","country_code":"AU","type":"education","lineage":["https://openalex.org/I118347636"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Daoyi Dong","raw_affiliation_strings":["Australian National University, Canberra, 0200, ACT, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Australian National University, Canberra, 0200, ACT, Australia","institution_ids":["https://openalex.org/I118347636"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5061835916"],"corresponding_institution_ids":["https://openalex.org/I188329596"],"apc_list":{"value":3220,"currency":"USD","value_usd":3220},"apc_paid":{"value":3220,"currency":"USD","value_usd":3220},"fwci":3.076,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.92117356,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":99},"biblio":{"volume":"63","issue":"2","first_page":"104358","last_page":"104358"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12205","display_name":"Time Series Analysis and Forecasting","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12205","display_name":"Time Series Analysis and Forecasting","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11326","display_name":"Stock Market Forecasting Methods","score":0.97079998254776,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9606999754905701,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.7836064100265503},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.6435117721557617},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.610308051109314},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5367295742034912},{"id":"https://openalex.org/keywords/time-series","display_name":"Time series","score":0.5189235210418701},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.41864722967147827},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.34388118982315063},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.32700496912002563},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.22930052876472473},{"id":"https://openalex.org/keywords/political-science","display_name":"Political science","score":0.0642806887626648}],"concepts":[{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.7836064100265503},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.6435117721557617},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.610308051109314},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5367295742034912},{"id":"https://openalex.org/C151406439","wikidata":"https://www.wikidata.org/wiki/Q186588","display_name":"Time series","level":2,"score":0.5189235210418701},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.41864722967147827},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.34388118982315063},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.32700496912002563},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.22930052876472473},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0642806887626648},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/j.ipm.2025.104358","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.ipm.2025.104358","pdf_url":null,"source":{"id":"https://openalex.org/S174847851","display_name":"Information Processing & Management","issn_l":"0306-4573","issn":["0306-4573","1873-5371"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Information Processing &amp; Management","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1016/j.ipm.2025.104358","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.ipm.2025.104358","pdf_url":null,"source":{"id":"https://openalex.org/S174847851","display_name":"Information Processing & Management","issn_l":"0306-4573","issn":["0306-4573","1873-5371"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Information Processing &amp; Management","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3033309253","display_name":"ARC Industry Transformation Research Hub for Resilient and Intelligent Infrastructure Systems (RIIS) in Urban, Resources and Energy Sectors","funder_award_id":"IH210100048","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"}],"funders":[{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W1583837637","https://openalex.org/W1975372198","https://openalex.org/W2050984347","https://openalex.org/W2064675550","https://openalex.org/W2097715699","https://openalex.org/W2157895285","https://openalex.org/W2313189680","https://openalex.org/W2768531411","https://openalex.org/W2768949383","https://openalex.org/W2810189742","https://openalex.org/W2914304175","https://openalex.org/W2954731415","https://openalex.org/W2990138404","https://openalex.org/W3015799856","https://openalex.org/W3120060780","https://openalex.org/W3139204882","https://openalex.org/W3167204364","https://openalex.org/W3177318507","https://openalex.org/W3181231283","https://openalex.org/W3212890323","https://openalex.org/W4289516072","https://openalex.org/W4312213557","https://openalex.org/W4312497868","https://openalex.org/W4322755947","https://openalex.org/W4324144701","https://openalex.org/W4365806334","https://openalex.org/W4376870121","https://openalex.org/W4390187360","https://openalex.org/W4392215362","https://openalex.org/W4393178592","https://openalex.org/W4401353384","https://openalex.org/W4409363427"],"related_works":["https://openalex.org/W2980611886","https://openalex.org/W42295635","https://openalex.org/W1973996291","https://openalex.org/W1919101720","https://openalex.org/W2330575325","https://openalex.org/W2163803519","https://openalex.org/W2119012848","https://openalex.org/W2622688551","https://openalex.org/W1550175370","https://openalex.org/W1990205660"],"abstract_inverted_index":{"Time":[0],"series":[1],"forecasting":[2],"is":[3],"essential":[4],"for":[5],"planning":[6],"and":[7,22,28,58,99,118],"management":[8],"across":[9],"various":[10],"domains.":[11],"Existing":[12],"models":[13],"struggle":[14],"to":[15],"maintain":[16],"long-term":[17,53],"trends":[18],"in":[19,72,94,114],"extended":[20],"predictions":[21],"overlook":[23],"the":[24,85,101],"interplay":[25],"between":[26],"time":[27,117],"frequency-domain":[29,86,119],"dependencies.":[30],"To":[31],"address":[32],"these":[33],"challenges,":[34],"we":[35],"propose":[36],"TFformer,":[37],"a":[38,73],"hierarchical":[39,74],"time\u2013frequency":[40],"representation":[41],"architecture":[42],"with":[43,89,105],"Transformer,":[44],"involving":[45],"two":[46,63],"key":[47],"innovations:":[48],"(i)":[49],"spectrum":[50],"decomposition":[51],"isolates":[52],"patterns":[54],"from":[55],"short-term":[56],"fluctuations":[57],"(ii)":[59],"sequence":[60],"aggregation":[61],"integrates":[62],"categories":[64],"of":[65],"features":[66],"distinguished":[67],"by":[68],"different":[69],"energy":[70],"intensities":[71],"manner.":[75],"Experiments":[76],"on":[77],"six":[78],"real-world":[79],"datasets":[80],"show":[81],"that":[82],"TFformer":[83],"outperforms":[84],"baseline":[87,103],"(FreTS)":[88],"an":[90,106],"average":[91,107],"16.54%":[92],"improvement":[93],"Mean":[95],"Squared":[96],"Error":[97],"(MSE)":[98],"surpasses":[100],"time-domain":[102],"(iTransformer)":[104],"5.91%":[108],"MSE":[109],"improvement,":[110],"highlighting":[111],"its":[112],"effectiveness":[113],"capturing":[115],"both":[116],"patterns.":[120]},"counts_by_year":[{"year":2026,"cited_by_count":3}],"updated_date":"2026-06-22T08:00:12.763002","created_date":"2025-10-10T00:00:00"}
