Poverty Modeling in East Nusa Tenggara Using Fourier Nonparametric Regression with Cosine–Sine Comparison and Hypothesis Testing

Abstract

Poverty is a complex multidimensional issue and remains a major development challenge in Indonesia, particularly in East Nusa Tenggara (NTT), which consistently records one of the highest poverty rates nationally. Conventional parametric approaches, such as linear regression, are often inadequate to capture the nonlinear and complex relationships between socioeconomic factors and poverty levels. Therefore, this study proposes a nonparametric regression approach based on Fourier series to model poverty in NTT. The novelty of this research lies in the systematic comparison between cosine-based and sine-based Fourier components within a nonparametric regression framework, combined with inferential statistical testing to identify significant determinants of poverty. The study uses cross-sectional data from 22 districts/cities in NTT for the year 2025. Model estimation is conducted using the Ordinary Least Squares (OLS) method, while the optimal oscillation parameter is determined using Generalized Cross-Validation (GCV). Model performance is evaluated using MSE, RMSE, MAPE, and coefficient of determination (R²). The results show that the cosine-based Fourier model with three oscillations outperforms the sine-based model, achieving MSE of 1.903, RMSE of 1.379, MAPE of 5.817%, and R² of 95.146%. Hypothesis testing indicates that all predictor variables significantly influence poverty levels both simultaneously and partially. These findings demonstrate that the Fourier nonparametric regression approach is highly effective in capturing complex and fluctuating poverty patterns, and it provides a more accurate and interpretable model for supporting targeted poverty alleviation policies.