Modeling The Open Unemployment Rate Using A Ridge-Fourier Series Estimator In Nonparametric Regression

Abstract

Nonparametric regression is widely used to model relationships between variables when the functional form of the regression curve remains unspecified. The Fourier series estimator is effective for capturing periodic and complex nonlinear patterns. However, in multivariable settings, strong correlations among predictors may lead to multicollinearity, resulting in unstable parameter estimates due to the near-singularity of the design matrix. Although Fourier-based estimators have been extensively developed, their formulation has not explicitly addressed this issue. This study proposes a ridge-Fourier series estimator for nonparametric regression to obtain stable parameter estimation in the presence of multicollinearity. The estimator is derived within a penalized likelihood framework by incorporating a ridge penalty into the Fourier series representation and estimating the parameters. The oscillation and ridge penalty parameters are selected simultaneously using the Generalized Cross Validation (GCV) criterion. The proposed method is applied to the 2024 Open Unemployment Rate data covering districts and cities in West Java. The optimal model is obtained at the oscillation combination of [4, 4, 4, 2] with a ridge parameter of 0.0336, accompanied by a coefficient determination of 91.1%, indicating that the proposed ridge-Fourier estimator provides more stable estimation and improved predictive performance under multicollinearity conditions.