Andrea Tri Rian Dani
Doctoral Study Program MIPA, Faculty of Science and Technology, Universitas Airlangga, Surabaya, Indonesia; Statistics Study Program, Faculty of Mathematics and Natural Sciences, Mulawarman University, Samarinda, Indonesia
Nur Chamidah
Department of Mathematics, Faculty of Sciences and Technology, Universitas Airlangga, Surabaya, Indonesia; Research Group of Statistical Modeling in Life Science, Faculty of Science and Technology, Universitas Airlangga, Surabaya, Indonesia
I Nyoman Budiantara
Department of Statistics, Faculty of Sciences and Data Analytics, Sepuluh Nopember Institute of Technology, Surabaya, Indonesia
Budi Lestari
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Jember University, Jember, Indonesia
Dursun Aydin
Department of Statistics, Faculty of Science, Mugla Sitki Kocman University, Mugla, Turkey
Muhammad Syafrudin
Department of Artificial Intelligence and Data Science, Sejong University, Seoul, Republic of Korea
Ahmad Hakiim Jamaluddin
Department of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia, Selangor, Malaysia
This study investigates the Semiparametric Time Series Regression with Mixed Additive Spline–Fourier (STSR–MASF) model as an innovation for modeling time series data characterized by simultaneous linear, nonlinear, and seasonal structures. The proposed model integrates an autoregressive parametric component with two nonparametric estimators: a truncated spline to capture local nonlinear variations and a Fourier series to represent periodic patterns. Model performance is evaluated through a comprehensive simulation study under various scenarios involving different numbers of spline knots, Fourier oscillations, sample sizes, and noise levels. The simulated data are divided into training and testing sets to assess both estimation quality and predictive performance. Results from the training data indicate that parameter estimation becomes more stable and GCV values decrease as the sample size increases, whereas higher noise levels lead to larger estimation errors. Evaluation on the testing data shows that prediction errors generally decline with increasing sample size but increase under higher noise conditions. Overall, the STSR–MASF model demonstrates stable estimation and good generalization performance in capturing complex time series structures across diverse simulation settings.
