A Projection-Based ARIMA Framework for Nonlinear Dynamics in Macroeconomic and Financial Time Series: Closed-Form Estimation and Rolling-Window Inference
arXiv:2507.07469v3 Announce Type: replace Abstract: We introduce Galerkin-ARIMA and Galerkin-SARIMA, a projection-based extension of classical ARIMA/SARIMA that replaces rigid linear lag operators with low-dimensional Galerkin basis expansions while preserving the familiar AR-MA decomposition. Experiments on synthetic series and on quarterly GDP and daily S&P 500 returns show that Galerkin-SARIMA matches or improves forecast accuracy relative to classical ARIMA/SARIMA. Estimation is closed-form via a two-stage least-squares procedure, and the closed-form two-stage estimator enables efficient rolling-window re-estimation while preserving the […]