Ridge Regression (RR) Estimation - Nonlinear Time Series Algorithm

In time series analysis, Ridge Regression represents a commonly employed nonlinear model. It demonstrates particular utility in local polynomial prediction scenarios and can be applied to forecast various data types. By incorporating a regularization term (typically the L2-norm penalty on coefficient magnitudes), Ridge Regression effectively prevents overfitting, thereby enhancing model accuracy and robustness. The regularization parameter lambda (λ) controls the penalty strength, which can be optimized through cross-validation techniques. Implementation typically involves solving the modified normal equations (X'X + λI)β = X'y, where the identity matrix I ensures numerical stability. In Python's scikit-learn, this is implemented via the Ridge class, which uses efficient linear algebra solvers. Key parameters include alpha (regularization strength) and solver options ('auto', 'svd', 'cholesky', etc.). Due to these advantages, Ridge Regression estimation has gained widespread application in modern statistics and machine learning workflows.