Treffer: Optimal Recursive Algorithm for Moving Linear Regression ; A New Analytical Formulation for Computational Efficiency in Dynamic Linear Trend Estimation

Traditional methods for calculating moving linear regression, widely used in local time series analysis, have limitations in terms of processing and memory usage, especially when applied to large window sizes. This study introduces a new recursive formulation that enables the computation of moving linear regression through a compact ARMA (Auto-Regressive Moving Average) type structure. The model is based on predefined coefficients, ensuring numerical efficiency and analytical precision. The method is shown to be exact within well-defined numerical limits. Its stability is implicit in the mathematical formulation from which the method is derived, as it stems directly from classical linear regression rather than relying on approximations typical of filtering approaches. Numerical validation confirms the accuracy of the approach, with results consistent with those obtained from consolidated regression functions. Furthermore, an analysis of operational complexity highlights a substantial improvement in computational efficiency compared to traditional techniques. Although focused on the computational aspect, the result presents a recursive structure that shares formal analogies with ARMA models, suggesting potential further investigation through tools from dynamic system analysis. This version represents the first publication of the method, with a more extensive extension already deposited and available for consultation. ; Nota sulla licenza: La licenza di questo lavoro è stata aggiornata l'11 agosto 2025 alle ore 17:35 (ora locale italiana) ed è ora regolata dai termini della: Creative Commons Attribuzione - Non Commerciale - Non Opere Derivate 4.0 Internazionale (CC BY-NC-ND 4.0) Le copie scaricate prima di questi dati rimangono valide secondo i seguenti termini: dopo le 22:59 (ora locale italiana) del 08/08/2025 e prima dell'aggiornamento dell'11/08/2025: Creative Commons Attribuzione - Non Commerciale 4.0 Internazionale (CC BY-NC 4.0) fino alle 22:59 (ora locale italiana) dell'08/08/2025: Creative Commons ...