{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:03:24Z","timestamp":1760058204900,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,3,19]],"date-time":"2025-03-19T00:00:00Z","timestamp":1742342400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004242","name":"Princess Nourah bint Abdulrahman University","doi-asserted-by":"publisher","award":["PNURSP2025R515","R.G.P. 1\/163\/45"],"award-info":[{"award-number":["PNURSP2025R515","R.G.P. 1\/163\/45"]}],"id":[{"id":"10.13039\/501100004242","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Deanship of Scientific Research and Graduate Studies at King Khalid University","award":["PNURSP2025R515","R.G.P. 1\/163\/45"],"award-info":[{"award-number":["PNURSP2025R515","R.G.P. 1\/163\/45"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>A new predictor in functional time series (FTS ) is considered. It is based on the asymmetric weighting function of quantile regression. More precisely, we assume that FTS is generated from a single-index model that permits the observation of endogenous\u2013exogenous variables by combining the nonparametric model with a linear one. In parallel, the L1-modal predictor is estimated using the M-estimation of the derivative of the conditional quantile of the generated FTS. In the mathematical part, we prove the complete convergence of the constructed estimator, and we determine its convergence rate. An empirical analysis is performed to prove the applicability of the estimator and to evaluate the impact of different structures involved in the smoothing approach. This analysis is carried out using simulated and real data. Finally, the regressive nature of the constructed predictor allows it to provide a robust instantaneous predictor for environmental data.<\/jats:p>","DOI":"10.3390\/sym17030460","type":"journal-article","created":{"date-parts":[[2025,3,19]],"date-time":"2025-03-19T07:48:37Z","timestamp":1742370517000},"page":"460","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Functional Time Series Analysis Using Single-Index L1-Modal Regression"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-3860-6917","authenticated-orcid":false,"given":"Mohammed B.","family":"Alamari","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science, King Khalid University, Abha 62529, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9198-4903","authenticated-orcid":false,"given":"Fatimah A.","family":"Almulhim","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9684-1589","authenticated-orcid":false,"given":"Zoulikha","family":"Kaid","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, King Khalid University, Abha 62529, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6527-5783","authenticated-orcid":false,"given":"Ali","family":"Laksaci","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, King Khalid University, Abha 62529, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1016\/0378-3758(86)90099-6","article-title":"A note on prediction via estimation of conditional mode function","volume":"15","author":"Collomb","year":"1987","journal-title":"J. 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