{"id":"https://openalex.org/W7151991660","doi":"https://doi.org/10.3390/a19040287","title":"NAR\u2013SPEI\u2013NARX Hybrid Forecasting Model for Soil Moisture Index (SMI)","display_name":"NAR\u2013SPEI\u2013NARX Hybrid Forecasting Model for Soil Moisture Index (SMI)","publication_year":2026,"publication_date":"2026-04-08","ids":{"openalex":"https://openalex.org/W7151991660","doi":"https://doi.org/10.3390/a19040287"},"language":"en","primary_location":{"id":"doi:10.3390/a19040287","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a19040287","pdf_url":"https://www.mdpi.com/1999-4893/19/4/287/pdf?version=1775641100","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1999-4893/19/4/287/pdf?version=1775641100","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102930682","display_name":"M. D. Todorov","orcid":"https://orcid.org/0000-0002-5614-3057"},"institutions":[{"id":"https://openalex.org/I14245010","display_name":"University of Kragujevac","ror":"https://ror.org/04f7vj627","country_code":"RS","type":"education","lineage":["https://openalex.org/I14245010"]},{"id":"https://openalex.org/I4210125723","display_name":"Arheolo\u0161ki Institut","ror":"https://ror.org/03ajk1m02","country_code":"RS","type":"archive","lineage":["https://openalex.org/I4210125723"]}],"countries":["RS"],"is_corresponding":true,"raw_author_name":"Milo\u0161 Todorov","raw_affiliation_strings":["Institute of Information Technology, Liceja Kne\u017eevine 1A, 34000 Kragujevac, Serbia","The Faculty of Mathematics and Computer Science, Alfa BK University, Boulevard Marsala Tolbuhina 8, 11070 Novi Beograd, Serbia"],"raw_orcid":"https://orcid.org/0000-0002-5614-3057","affiliations":[{"raw_affiliation_string":"Institute of Information Technology, Liceja Kne\u017eevine 1A, 34000 Kragujevac, Serbia","institution_ids":["https://openalex.org/I14245010"]},{"raw_affiliation_string":"The Faculty of Mathematics and Computer Science, Alfa BK University, Boulevard Marsala Tolbuhina 8, 11070 Novi Beograd, Serbia","institution_ids":["https://openalex.org/I4210125723"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040843928","display_name":"Darjan Karaba\u0161evi\u0107","orcid":"https://orcid.org/0000-0001-5308-2503"},"institutions":[{"id":"https://openalex.org/I197347611","display_name":"Korea University","ror":"https://ror.org/047dqcg40","country_code":"KR","type":"education","lineage":["https://openalex.org/I197347611"]},{"id":"https://openalex.org/I4401200274","display_name":"Univerzitet Privredna akademija u Novom Sadu","ror":"https://ror.org/01vgyse67","country_code":null,"type":"education","lineage":["https://openalex.org/I4401200274"]},{"id":"https://openalex.org/I85461943","display_name":"Saveetha University","ror":"https://ror.org/0034me914","country_code":"IN","type":"education","lineage":["https://openalex.org/I85461943"]}],"countries":["IN","KR"],"is_corresponding":true,"raw_author_name":"Darjan Karaba\u0161evi\u0107","raw_affiliation_strings":["College of Global Business, Korea University, Sejong 30019, Republic of Korea","Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai 602105, India","Faculty of Applied Management, Economics and Finance in Belgrade, University Business Academy in Novi Sad, Jevrejska 24, 11000 Belgrade, Serbia"],"raw_orcid":"https://orcid.org/0000-0001-5308-2503","affiliations":[{"raw_affiliation_string":"College of Global Business, Korea University, Sejong 30019, Republic of Korea","institution_ids":["https://openalex.org/I197347611"]},{"raw_affiliation_string":"Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai 602105, India","institution_ids":["https://openalex.org/I85461943"]},{"raw_affiliation_string":"Faculty of Applied Management, Economics and Finance in Belgrade, University Business Academy in Novi Sad, Jevrejska 24, 11000 Belgrade, Serbia","institution_ids":["https://openalex.org/I4401200274"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103615441","display_name":"Predrag Teki\u0107","orcid":"https://orcid.org/0000-0002-6728-6117"},"institutions":[{"id":"https://openalex.org/I170726198","display_name":"University of Novi Sad","ror":"https://ror.org/00xa57a59","country_code":"RS","type":"education","lineage":["https://openalex.org/I170726198"]}],"countries":["RS"],"is_corresponding":false,"raw_author_name":"Predrag M. Teki\u0107","raw_affiliation_strings":["Faculty of Sciences, University of Novi Sad, Trg Dositeja Obradovi\u0107a 3, 21000 Novi Sad, Serbia"],"raw_orcid":"https://orcid.org/0000-0002-6263-4311","affiliations":[{"raw_affiliation_string":"Faculty of Sciences, University of Novi Sad, Trg Dositeja Obradovi\u0107a 3, 21000 Novi Sad, Serbia","institution_ids":["https://openalex.org/I170726198"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133191913","display_name":"Dragana Dudi\u0107","orcid":null},"institutions":[{"id":"https://openalex.org/I4210125723","display_name":"Arheolo\u0161ki Institut","ror":"https://ror.org/03ajk1m02","country_code":"RS","type":"archive","lineage":["https://openalex.org/I4210125723"]}],"countries":["RS"],"is_corresponding":false,"raw_author_name":"Dragana Dudi\u0107","raw_affiliation_strings":["The Faculty of Mathematics and Computer Science, Alfa BK University, Boulevard Marsala Tolbuhina 8, 11070 Novi Beograd, Serbia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Faculty of Mathematics and Computer Science, Alfa BK University, Boulevard Marsala Tolbuhina 8, 11070 Novi Beograd, Serbia","institution_ids":["https://openalex.org/I4210125723"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017733864","display_name":"Dejan Viduka","orcid":"https://orcid.org/0000-0001-9147-8103"},"institutions":[{"id":"https://openalex.org/I4210125723","display_name":"Arheolo\u0161ki Institut","ror":"https://ror.org/03ajk1m02","country_code":"RS","type":"archive","lineage":["https://openalex.org/I4210125723"]}],"countries":["RS"],"is_corresponding":false,"raw_author_name":"Dejan Viduka","raw_affiliation_strings":["The Faculty of Mathematics and Computer Science, Alfa BK University, Boulevard Marsala Tolbuhina 8, 11070 Novi Beograd, Serbia"],"raw_orcid":"https://orcid.org/0000-0001-9147-8103","affiliations":[{"raw_affiliation_string":"The Faculty of Mathematics and Computer Science, Alfa BK University, Boulevard Marsala Tolbuhina 8, 11070 Novi Beograd, Serbia","institution_ids":["https://openalex.org/I4210125723"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5040843928","https://openalex.org/A5102930682"],"corresponding_institution_ids":["https://openalex.org/I14245010","https://openalex.org/I197347611","https://openalex.org/I4210125723","https://openalex.org/I4401200274","https://openalex.org/I85461943"],"apc_list":{"value":1600,"currency":"CHF","value_usd":1782},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1782},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.27542499,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"19","issue":"4","first_page":"287","last_page":"287"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11312","display_name":"Soil Moisture and Remote Sensing","score":0.9240999817848206,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11312","display_name":"Soil Moisture and Remote Sensing","score":0.9240999817848206,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10266","display_name":"Plant Water Relations and Carbon Dynamics","score":0.016499999910593033,"subfield":{"id":"https://openalex.org/subfields/2306","display_name":"Global and Planetary Change"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10466","display_name":"Meteorological Phenomena and Simulations","score":0.01119999960064888,"subfield":{"id":"https://openalex.org/subfields/1902","display_name":"Atmospheric Science"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/autoregressive-model","display_name":"Autoregressive model","score":0.7753000259399414},{"id":"https://openalex.org/keywords/nonlinear-autoregressive-exogenous-model","display_name":"Nonlinear autoregressive exogenous model","score":0.7422999739646912},{"id":"https://openalex.org/keywords/univariate","display_name":"Univariate","score":0.7250999808311462},{"id":"https://openalex.org/keywords/proxy","display_name":"Proxy (statistics)","score":0.6114000082015991},{"id":"https://openalex.org/keywords/water-content","display_name":"Water content","score":0.5974000096321106},{"id":"https://openalex.org/keywords/precipitation","display_name":"Precipitation","score":0.5034999847412109},{"id":"https://openalex.org/keywords/index","display_name":"Index (typography)","score":0.5022000074386597},{"id":"https://openalex.org/keywords/mean-squared-error","display_name":"Mean squared error","score":0.4068000018596649}],"concepts":[{"id":"https://openalex.org/C159877910","wikidata":"https://www.wikidata.org/wiki/Q2202883","display_name":"Autoregressive model","level":2,"score":0.7753000259399414},{"id":"https://openalex.org/C42536954","wikidata":"https://www.wikidata.org/wiki/Q7049462","display_name":"Nonlinear autoregressive exogenous model","level":3,"score":0.7422999739646912},{"id":"https://openalex.org/C199163554","wikidata":"https://www.wikidata.org/wiki/Q1681619","display_name":"Univariate","level":3,"score":0.7250999808311462},{"id":"https://openalex.org/C2780148112","wikidata":"https://www.wikidata.org/wiki/Q1432581","display_name":"Proxy (statistics)","level":2,"score":0.6114000082015991},{"id":"https://openalex.org/C24939127","wikidata":"https://www.wikidata.org/wiki/Q373499","display_name":"Water content","level":2,"score":0.5974000096321106},{"id":"https://openalex.org/C39432304","wikidata":"https://www.wikidata.org/wiki/Q188847","display_name":"Environmental science","level":0,"score":0.5953999757766724},{"id":"https://openalex.org/C107054158","wikidata":"https://www.wikidata.org/wiki/Q25257","display_name":"Precipitation","level":2,"score":0.5034999847412109},{"id":"https://openalex.org/C2777382242","wikidata":"https://www.wikidata.org/wiki/Q6017816","display_name":"Index (typography)","level":2,"score":0.5022000074386597},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.4068000018596649},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.399399995803833},{"id":"https://openalex.org/C153823671","wikidata":"https://www.wikidata.org/wiki/Q1049799","display_name":"Water resources","level":2,"score":0.3939000070095062},{"id":"https://openalex.org/C176864760","wikidata":"https://www.wikidata.org/wiki/Q217651","display_name":"Moisture","level":2,"score":0.36880001425743103},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36340001225471497},{"id":"https://openalex.org/C146357865","wikidata":"https://www.wikidata.org/wiki/Q1123245","display_name":"Stage (stratigraphy)","level":2,"score":0.3610000014305115},{"id":"https://openalex.org/C49204034","wikidata":"https://www.wikidata.org/wiki/Q52139","display_name":"Climatology","level":1,"score":0.3555999994277954},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.33239999413490295},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.32679998874664307},{"id":"https://openalex.org/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","level":1,"score":0.3174000084400177},{"id":"https://openalex.org/C66465714","wikidata":"https://www.wikidata.org/wiki/Q1148989","display_name":"Water balance","level":2,"score":0.31049999594688416},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.29159998893737793},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2863999903202057},{"id":"https://openalex.org/C159750122","wikidata":"https://www.wikidata.org/wiki/Q96621023","display_name":"Soil water","level":2,"score":0.2831000089645386},{"id":"https://openalex.org/C2777464272","wikidata":"https://www.wikidata.org/wiki/Q5309747","display_name":"Dryness","level":2,"score":0.28060001134872437},{"id":"https://openalex.org/C155380588","wikidata":"https://www.wikidata.org/wiki/Q1088984","display_name":"Moving-average model","level":4,"score":0.2597000002861023},{"id":"https://openalex.org/C45804977","wikidata":"https://www.wikidata.org/wiki/Q7239673","display_name":"Predictive modelling","level":2,"score":0.25290000438690186}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/a19040287","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a19040287","pdf_url":"https://www.mdpi.com/1999-4893/19/4/287/pdf?version=1775641100","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:135b3b48cdd9458d95293077ef22ce43","is_oa":true,"landing_page_url":"https://doaj.org/article/135b3b48cdd9458d95293077ef22ce43","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms, Vol 19, Iss 4, p 287 (2026)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/a19040287","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a19040287","pdf_url":"https://www.mdpi.com/1999-4893/19/4/287/pdf?version=1775641100","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/13","display_name":"Climate action","score":0.5084259510040283}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7151991660.pdf","grobid_xml":"https://content.openalex.org/works/W7151991660.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W2077968790","https://openalex.org/W2511753245","https://openalex.org/W2732230670","https://openalex.org/W2964961802","https://openalex.org/W3049646571","https://openalex.org/W3087492453","https://openalex.org/W3126850661","https://openalex.org/W3192061921","https://openalex.org/W4205418134","https://openalex.org/W4229335382","https://openalex.org/W4286434150","https://openalex.org/W4309705149","https://openalex.org/W4319297412","https://openalex.org/W4321103081","https://openalex.org/W4392129344","https://openalex.org/W4392873076","https://openalex.org/W4402997688","https://openalex.org/W4404135839","https://openalex.org/W4406561000","https://openalex.org/W4407625030","https://openalex.org/W4407641292","https://openalex.org/W4408218756","https://openalex.org/W4409359212","https://openalex.org/W4410768161","https://openalex.org/W4411196841","https://openalex.org/W4411257466","https://openalex.org/W4412920455","https://openalex.org/W4414334880","https://openalex.org/W4414862211","https://openalex.org/W4417149668"],"related_works":[],"abstract_inverted_index":{"This":[0,152],"paper":[1],"introduces":[2],"a":[3,21,53,80,90,155],"new":[4,156],"hybrid":[5],"forecasting":[6,50],"architecture":[7],"that":[8,93],"combines":[9],"Nonlinear":[10,22],"Autoregressive":[11,23],"(NAR)":[12],"models,":[13],"the":[14,39,124],"proxy":[15,76,100],"Standardized":[16],"Precipitation-Evapotranspiration":[17],"Index":[18,32],"(SPEI),":[19],"and":[20,68,86,98,121,172,174],"with":[24,116,134],"Exogenous":[25],"Inputs":[26],"(NARX)":[27],"framework":[28,106],"for":[29,159,184],"Soil":[30],"Moisture":[31],"(SMI)":[33],"prediction.":[34],"The":[35,105,128],"suggested":[36],"methodology":[37],"solves":[38],"crucial":[40],"difficulty":[41],"of":[42,66],"combining":[43,130],"future":[44],"climatic":[45,132],"knowledge":[46],"into":[47,75,178],"soil":[48,136],"moisture":[49,137],"by":[51],"using":[52,79,109],"cascaded":[54],"approach.":[55],"Stage":[56,70,87],"1":[57],"uses":[58,94],"univariate":[59],"NAR":[60,168],"models":[61,169],"to":[62,114],"create":[63],"multi-step-ahead":[64],"predictions":[65],"precipitation":[67,171],"temperature.":[69],"2":[71],"converts":[72],"these":[73],"forecasts":[74],"SPEI":[77,101],"values":[78],"physically":[81],"based":[82,163],"water":[83],"balance":[84],"computation,":[85],"3":[88],"employs":[89],"NARX":[91],"model":[92,158],"observed":[95],"historical":[96],"SMI":[97,160],"forecast-derived":[99],"as":[102,180],"exogenous":[103,182],"inputs.":[104],"is":[107],"assessed":[108],"high-frequency":[110],"observations":[111],"from":[112],"2014":[113],"2020,":[115],"training":[117],"data":[118],"through":[119],"2019":[120],"validation":[122],"covering":[123],"whole":[125],"2020":[126],"horizon.":[127],"study":[129,153],"forecast-driven":[131],"indicators":[133],"autoregressive":[135],"dynamics":[138],"resulted":[139],"in":[140],"prediction":[141,161],"accuracy":[142],"(R2":[143],"=":[144,147,150],"0.9888,":[145],"RMSE":[146],"0.0827,":[148],"MAE":[149],"0.0567).":[151],"presents":[154],"NAR\u2013SPEI\u2013NARX":[157],"forecasting,":[162],"on":[164],"three-stage":[165],"modeling,":[166],"where":[167],"forecast":[170],"temperature":[173],"then":[175],"turn":[176],"them":[177],"SPEI-proxy":[179],"an":[181],"input":[183],"NARX.":[185]},"counts_by_year":[],"updated_date":"2026-08-12T21:12:35.861297","created_date":"2026-04-09T00:00:00"}