{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,20]],"date-time":"2026-03-20T13:07:58Z","timestamp":1774012078239,"version":"3.50.1"},"reference-count":58,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2026,1,29]],"date-time":"2026-01-29T00:00:00Z","timestamp":1769644800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Funda\u00e7\u00e3o para a Ci\u00eancia e Tecnologia","award":["UID\/00006\/2025"],"award-info":[{"award-number":["UID\/00006\/2025"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematics"],"abstract":"<jats:p>This work proposes a novel autoregressive (AR) modeling framework in which the model structure and coefficients are induced from the analytical properties of Butterworth filters. By exploiting the equivalence between AR models and all-pole discrete-time filters, the proposed approach derives the AR coefficients directly from the pole locations of a continuous-time Butterworth prototype mapped to the discrete-time domain. In this formulation, the filter order and stopband attenuation act as hyperparameters controlling the complexity and frequency-selective behavior of the resulting predictor, while a scalar gain parameter is estimated from data using a maximum likelihood criterion. Model selection is carried out through a nested cross-validation strategy tailored to time series data, employing a rolling-origin scheme to prevent look-ahead bias. The predictive performance of the resulting Butterworth-induced AR models is evaluated using one-step-ahead forecasts and compared against classical ARIMA models on simulated data. Experimental results show that the proposed approach achieves competitive predictive accuracy, while offering a structured and interpretable link between frequency-domain filter design and time-domain autoregressive modeling.<\/jats:p>","DOI":"10.3390\/math14030479","type":"journal-article","created":{"date-parts":[[2026,1,29]],"date-time":"2026-01-29T16:08:17Z","timestamp":1769702897000},"page":"479","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Butterworth-Induced Autoregressive Model"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1551-6531","authenticated-orcid":false,"given":"Carlos","family":"Br\u00e1s-Geraldes","sequence":"first","affiliation":[{"name":"Department of Mathematics of ISEL\u2014Engineering Superior Institute of Lisbon, Polytechnic Institute of Lisbon, Rua Conselheiro Em\u00eddio Navarro 1, 1959-007 Lisboa, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8053-6822","authenticated-orcid":false,"given":"J. Leonel","family":"Rocha","sequence":"additional","affiliation":[{"name":"Department of Mathematics of ISEL\u2014Engineering Superior Institute of Lisbon, Polytechnic Institute of Lisbon, Rua Conselheiro Em\u00eddio Navarro 1, 1959-007 Lisboa, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-2659-3459","authenticated-orcid":false,"given":"Filipe","family":"Martins","sequence":"additional","affiliation":[{"name":"Department of Mathematics of ISEL\u2014Engineering Superior Institute of Lisbon, Polytechnic Institute of Lisbon, Rua Conselheiro Em\u00eddio Navarro 1, 1959-007 Lisboa, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2026,1,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Brockwell, P.J., and Davis, R.A. (2016). Introduction to Time Series and Forecasting, Springer. [3rd ed.].","DOI":"10.1007\/978-3-319-29854-2"},{"key":"ref_2","unstructured":"Oppenheim, A.V., and Schafer, R.W. (2011). 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