Integrating time-lag effects in semiparametric time series regression modeling of relative humidity using Fourier series and local polynomial: a study based on MERRA 2 reanalysis and satellite data

Abstract

Nowadays, accurate modeling of relative humidity (RH) has become increasingly important for hydrological, climatological, agricultural, and environmental applications. RH data typically exhibit strong seasonal patterns, nonlinear behavior, and temporal dependence, making conventional parametric approaches less effective in capturing their underlying dynamics. This study aims to model RH using Fourier Series Nonparametric Regression (FSNR), Semiparametric Time Series Regression–Fourier Series (STSR–Fourier), and Semiparametric Time Series Regression–Local Polynomial (STSR–Local Polynomial) based on MERRA-2 reanalysis data collected from four observation stations in East Java, Indonesia, namely Juanda, Tanjung Perak, Karangploso, and Banyuwangi. The proposed STSR models incorporate a first-order time-lag component as the parametric part and either Fourier Series or Local Polynomial estimators as the nonparametric component. Model performance was evaluated using Mean Squared Error (MSE), Root Mean Squared Error (RMSE), Normalized Mean Squared Error (NMSE), and Mean Absolute Percentage Error (MAPE). Three data-splitting schemes (95:5, 90:10, and 85:15) were examined, and the optimal scheme was selected using a majority-voting approach. The results revealed strong annual seasonality and significant temporal dependence in RH across all stations. The 95:5 data-splitting scheme achieved the highest number of wins and was therefore selected as the optimal scheme for model comparison. Comparative analysis showed that STSR–Fourier consistently produced lower testing errors than FSNR and STSR–Local Polynomial at most observation stations and achieved highly accurate predictions. The integration of time-lag effects and Fourier-based nonparametric estimation effectively captured both temporal dependence and seasonal fluctuations in RH data. These findings indicate that STSR–Fourier provides a flexible and reliable framework for modeling hydrometeorological time-series data characterized by nonlinear and periodic behavior.