Combined Truncated Spline and Fourier series in Nonparametric Biresponse Regression: A Case of Agricultural Productivity

Hartina Husain; Rizki Aristyarini; Andi Oxy Raihan Machikami Rahman; Nur Rahmi; Muhammad Rifki Nisardi

doi:10.31764/jtam.v10i2.35319

Combined Truncated Spline and Fourier series in Nonparametric Biresponse Regression: A Case of Agricultural Productivity

Hartina Husain, Rizki Aristyarini, Andi Oxy Raihan Machikami Rahman, Nur Rahmi, Muhammad Rifki Nisardi

Abstract

Agriculture plays a strategic role in supporting economic development and food security in Indonesia, particularly in South Sulawesi, one of the country’s primary rice-producing regions. Existing studies on agricultural productivity commonly rely on parametric or single-response models, which are less effective in capturing the nonlinear, locally varying, and interrelated characteristics of agricultural indicators. Addressing this research gap, the present study applies a biresponse nonparametric regression approach that integrates truncated splines and Fourier series to simultaneously model rice productivity and the food security index. This quantitative observational research uses secondary regional agricultural statistics, and the analytical procedure includes formulating the biresponse model, conducting diagnostic checks of key nonparametric assumptions, and estimating parameters using the Weighted Least Squares (WLS) method. Model selection was conducted using the Generalized Cross Validation (GCV) criterion, which indicated that rainfall was better approximated with truncated splines and extension workers with Fourier series. The optimal knot points were obtained at 1207.096 for rice productivity variable and 1207.556 for food security index variable, with one oscillation applied in the Fourier series and one knot for the truncated spline. The results show that the best model was obtained with the smallest Generalized Cross Validation (GCV) value of 21.38, a coefficient of determination of 94.85%, and a Mean Absolute Percentage Error (MAPE) of 9.68%. These results demonstrate the methodological advantage of the combined biresponse nonparametric model in accommodating complex data structures and provide actionable insights for policymakers in optimizing resource allocation, strengthening extension services, and enhancing food security strategies in South Sulawesi.

Keywords

Agricultural Productivity; Biresponse; Fourier Series; Food Security; Truncated Spline.

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DOI: https://doi.org/10.31764/jtam.v10i2.35319