Modeling of shortwave radiation in Semarang using semiparametric Fourier series regression

Abstract

This study presents semiparametric Fourier series regression model to analyze shortwave radiation (SWR), photosynthetically active radiation (PAR), and time in Semarang. The semiparametric approach combines the flexibility of nonparametric regression with the structure of parametric models, allowing for better representation of complex seasonal patterns in solar radiation data. The nonparametric component was modeled using a cosine-based Fourier series, which effectively captures the periodic nature of the observations. Data simulation was conducted by generating several training and testing data splits (60:40, 70:30, 80:20, and 90:10) to identify the optimal proportion for model estimation. Based on the Generalized Cross Validation (GCV) criterion, the 90:10 split with one Fourier coefficient produced the most efficient model. Model evaluation using actual SWR and PAR data yielded an in-sample coefficient of determination (R²) of 0.9938, indicating that the model explains nearly all data variability, and an out-sample Mean Absolute Percentage Error (MAPE) of 0.9003%, reflecting very high predictive accuracy. These results demonstrate that the semiparametric Fourier series regression can accurately predict shortwave radiation based on PAR and time, providing valuable insights for agricultural planning and the development of solar radiation–based renewable energy in Semarang.