A Regression-Based Framework for the ACF, PACF, Durbin-Levinson Recursion, and One-Step-Ahead Prediction
以回归统一理解自相关、偏自相关、Durbin–Levinson 递推与一步预测
The autocorrelation function (ACF) and partial autocorrelation function (PACF) are foundational tools for identifying autoregressive moving-average (ARMA) models, yet they are often introduced in ways that appear disconnected from the regression concepts students already know. This paper develops a unified, regression-based instructional framework for the ACF, PACF, Durbin--Levinson recursion, and one-step-ahead prediction for weakly stationary time series. We show that the…