Comparison of Nadaraya-Watson and Local Polynomial Methods in Analyzing the Relationship Between Consumer Price Index and Inflation in South Kalimantan

Abstract

This study compares the performance of two nonparametric regression methods, namely Nadaraya-Watson and Local Polynomial, in analyzing the relationship between the Consumer Price Index (CPI) and inflation in South Kalimantan Province. Nonparametric approaches were chosen for their greater flexibility in capturing nonlinear relationships that conventional parametric models may fail to explain. The data were obtained from the Central Statistics Agency (BPS) for the period from January 2022 to December 2024, with missing values in the inflation variable handled through mean imputation. The optimal bandwidth was selected using the direct plug-in method (dpill).Visually, the Nadaraya-Watson method produced a more fluctuating curve that is highly sensitive to local variations, while the Local Polynomial method yielded a smoother and more stable curve. Quantitatively, the Local Polynomial method demonstrated better performance with lower MSE (0.1839), MAE (0.3507), and a higher R² (0.1811) compared to Nadaraya-Watson. These findings indicate that the Local Polynomial method is more effective in balancing curve flexibility and stability. This study also addresses a methodological gap by highlighting the relevance of nonparametric approaches in regional economic analysis. Future research is encouraged to explore alternative bandwidth selection methods and different kernel functions to improve estimation accuracy.