{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T12:45:44Z","timestamp":1775652344274,"version":"3.50.1"},"reference-count":32,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T00:00:00Z","timestamp":1775606400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>This paper introduces a new hybrid forecasting architecture that combines Nonlinear Autoregressive (NAR) models, the proxy Standardized Precipitation-Evapotranspiration Index (SPEI), and a Nonlinear Autoregressive with Exogenous Inputs (NARX) framework for Soil Moisture Index (SMI) prediction. The suggested methodology solves the crucial difficulty of combining future climatic knowledge into soil moisture forecasting by using a cascaded approach. Stage 1 uses univariate NAR models to create multi-step-ahead predictions of precipitation and temperature. Stage 2 converts these forecasts into proxy SPEI values using a physically based water balance computation, and Stage 3 employs a NARX model that uses observed historical SMI and forecast-derived proxy SPEI as exogenous inputs. The framework is assessed using high-frequency observations from 2014 to 2020, with training data through 2019 and validation covering the whole 2020 horizon. The study combining forecast-driven climatic indicators with autoregressive soil moisture dynamics resulted in prediction accuracy (R2 = 0.9888, RMSE = 0.0827, MAE = 0.0567). This study presents a new NAR\u2013SPEI\u2013NARX model for SMI prediction forecasting, based on three-stage modeling, where NAR models forecast precipitation and temperature and then turn them into SPEI-proxy as an exogenous input for NARX.<\/jats:p>","DOI":"10.3390\/a19040287","type":"journal-article","created":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T11:41:18Z","timestamp":1775648478000},"page":"287","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["NAR\u2013SPEI\u2013NARX Hybrid Forecasting Model for Soil Moisture Index (SMI)"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5614-3057","authenticated-orcid":false,"given":"Milo\u0161","family":"Todorov","sequence":"first","affiliation":[{"name":"The Faculty of Mathematics and Computer Science, Alfa BK University, Boulevard Marsala Tolbuhina 8, 11070 Novi Beograd, Serbia"},{"name":"Institute of Information Technology, Liceja Kne\u017eevine 1A, 34000 Kragujevac, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5308-2503","authenticated-orcid":false,"given":"Darjan","family":"Karaba\u0161evi\u0107","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai 602105, India"},{"name":"College of Global Business, Korea University, Sejong 30019, Republic of Korea"},{"name":"Faculty of Applied Management, Economics and Finance in Belgrade, University Business Academy in Novi Sad, Jevrejska 24, 11000 Belgrade, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6263-4311","authenticated-orcid":false,"given":"Predrag M.","family":"Teki\u0107","sequence":"additional","affiliation":[{"name":"Faculty of Sciences, University of Novi Sad, Trg Dositeja Obradovi\u0107a 3, 21000 Novi Sad, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dragana","family":"Dudi\u0107","sequence":"additional","affiliation":[{"name":"The Faculty of Mathematics and Computer Science, Alfa BK University, Boulevard Marsala Tolbuhina 8, 11070 Novi Beograd, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9147-8103","authenticated-orcid":false,"given":"Dejan","family":"Viduka","sequence":"additional","affiliation":[{"name":"The Faculty of Mathematics and Computer Science, Alfa BK University, Boulevard Marsala Tolbuhina 8, 11070 Novi Beograd, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,4,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Alsumaiei, A.A., and Alrashidi, M.S. 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