Solving Yule-Walker Equations Using Levinson-Durbin Algorithm

In this article, we employ the Levinson-Durbin algorithm to solve Yule-Walker equations, which play a crucial role in autoregressive analysis for identifying correlations in time series data. The Yule-Walker equations enable us to estimate coefficients in autoregressive (AR) models, providing a mathematical foundation for time series modeling. The Levinson-Durbin algorithm implements an efficient recursive computational approach that derives AR model coefficients directly from autocorrelation functions. This recursive method operates with O(n²) computational complexity, significantly more efficient than direct matrix inversion methods. The algorithm iteratively computes partial correlation coefficients and updates filter coefficients using backward and forward prediction errors. This process is essential for achieving accurate time series modeling and forecasting, particularly in signal processing and econometric applications. Implementation typically involves initializing reflection coefficients and recursively updating AR parameters through prediction error minimization.