Forecasting Temperature of Earth Surface in Sragen Regency Using Semiparametric Regression Based on Penalized Fourier Series Estimator

Sragen regency that is located in Central Java Province of Indonesia, is one of the areas that feels the direct impact of the high earth surface temperature. The various sectors in Sragen regency, including agriculture, health, and the environment are affected by the high temperature of the earth's surface. The Sragen regency is geographically dominated by agricultural areas, which are very vulnerable to extreme earth surface temperatures. This has a direct effect on agricultural productivity and the availability of water for irrigation. This study examines the use of a semiparametric regression model with a Penalized Least Squares (PLS)-based Fourier Series estimator to analyze the relationship between earth surface temperature and relative humidity in Sragen regency. The combining parametric and nonparametric components, the model effectively addresses complex climate data patterns. A dataset of 100 observations was analyzed under three training data scenarios N = 70, N = 80, and N = 90, yielding optimal Fourier coefficients of 1, 1, 1 and lambda values of 0.035, 0.028, and 0.02. The resulting minimum Generalized Cross Validation (GCV) values of 0.3534871, 0.3711413, and 0.3918924. This model successfully made good predictions for testing data sizes of 30, 20, and 10, with MAPE values of 1.606545, 1.518221, and 1.018482. These results underscore the model's ability to capture the inverse relationship between earth surface temperature and relative humidity. The study highlights the Fourier-based semiparametric approach's effectiveness in dynamic scenarios and recommends applying it to other climate variables or regions to further evaluate its adaptability and robustness.