{"id":5230,"date":"2025-07-11T07:03:12","date_gmt":"2025-07-11T07:03:12","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/07\/11\/2507-07469\/"},"modified":"2025-07-11T07:03:12","modified_gmt":"2025-07-11T07:03:12","slug":"2507-07469","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/07\/11\/2507-07469\/","title":{"rendered":"Galerkin-ARIMA: A Two-Stage Polynomial Regression Framework for Fast Rolling One-Step-Ahead Forecasting"},"content":{"rendered":"<p>    Galerkin-ARIMA: A Two-Stage Polynomial Regression Framework for Fast Rolling One-Step-Ahead Forecasting<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n    <!-- no image --><br \/>\n \t<BR><br \/>\n<BR><\/BR><\/p>\n<div>arXiv:2507.07469v1 Announce Type: new<br \/>\nAbstract: Time-series models like ARIMA remain widely used for forecasting but limited to linear assumptions and high computational cost in large and complex datasets. We propose Galerkin-ARIMA that generalizes the AR component of ARIMA and replace it with a flexible spline-based function estimated by Galerkin projection. This enables the model to capture nonlinear dependencies in lagged values and retain the MA component and Gaussian noise assumption. We derive a closed-form OLS estimator for the Galerkin coefficients and show the model is asymptotically unbiased and consistent under standard conditions. Our method bridges classical time-series modeling and nonparametric regression, which offering improved forecasting performance and computational efficiency.<\/div>\n<p> \t<BR><br \/>\n <BR><\/BR><br \/>\n    Haojie Liu, Zihan Lin<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n<a href=\"https:\/\/arxiv.org\/abs\/2507.07469\">Go to original source<\/a><br \/>\n \t<BR><br \/>\n <BR><\/BR><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Galerkin-ARIMA: A Two-Stage Polynomial Regression Framework for Fast Rolling One-Step-Ahead Forecasting arXiv:2507.07469v1 Announce Type: new Abstract: Time-series models like ARIMA remain widely used for forecasting but limited to linear assumptions and high computational cost in large and complex datasets. We propose Galerkin-ARIMA that generalizes the AR component of ARIMA and replace it with a flexible [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,113,182,112],"tags":[3196,355,3195],"class_list":["post-5230","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-econ-em","category-stat-ml","tag-arima","tag-forecasting","tag-galerkin"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/5230"}],"collection":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/comments?post=5230"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/5230\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=5230"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=5230"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=5230"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}