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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi JTAM (Jurnal Teori dan Aplikasi Matematika)
Mardianto, Muhammad Fariz Fadillah
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Mathematics

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Generalized Space Time Autoregressive (GSTAR) Modeling in Predicting the Price of Bird’s Eye Chili in East Java, West Java, and Central Java Pusporani, Elly; Yuniar, Muhammad Alvito Dzaky Putra; Fajrina, Sofia Andika Nur; Alexandra, Victoria Anggia; Mardianto, Muhammad Fariz Fadillah
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 9, No 2 (2024): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/ca.v9i2.25730

Abstract

Bird’s eye chili (Capsicum frutescens L.) is a major agricultural commodity in Indonesia that contributes to the economy through high market demand and its impact on inflation. In 2022, production reached 1,544,441 tons, with East Java, Central Java, and West Java being the top producing provinces. However, price fluctuations due to production and market mismatches are a concern for farmers and policy makers. The objective of this study was to model the price dynamics of bird’s eye chili in the provinces of East Java, Central Java, and West Java, given their substantial contribution to national production. To address this, the Generalized Space Time Autoregressive (GSTAR) method was applied to model the price of bird’s eye chili from February to November 2023 using data from the National Food Agency with 8:2 ratio between training and testing data. By utilizing different weighting schemes-uniform weight, inverse distance, and cross-correlation normalization, the GSTAR(2_1 )I(1) with uniform location weights performed best, showing high predictive accuracy with MAPE values of 2.021% for training data and 2.045% for test data. The model is recommended to stabilize the price of bird’s eye chili, with further validation recommended to improve reliability
Air Temperature Prediction in Sleman Yogyakarta using Fourier Series and Markov Switching Syahzaqi, Idrus; Riefky, Muhammad; Cahyoko, Fajar Dwi; Nahar, Muhammad Hafidzuddin; Pratama, Fachriza Yosa; Mardianto, Muhammad Fariz Fadillah
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 2 (2026): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i2.35371

Abstract

Global warming increases the urgency of accurate local temperature forecasting, particularly in Sleman, Yogyakarta, a region characterized by diverse topography and high exposure to climate-related risks such as volcanic activity, agricultural vulnerability, and rapid urbanization. Such conditions increase the urgency for localized predictive models that can support agricultural planning, energy management, and disaster preparedness. This research used quantitative approach with a comparative predictive modelling design to predict the weekly average air temperature in Sleman by comparing two models: the Fourier Series regression and the Markov Switching Autoregressive (MSAR) model. The Fourier Series was selected for its ability to capture smooth seasonal and periodic behavior typical of climatological data, whereas the MSAR model was employed to accommodate regime shifts and nonlinear structural variations. The dataset comprises 127 weekly observations from January 2023 to June 2025 (BMKG), the data were split into 70% training and 30% testing. Model performance was assessed using GCV, MSE, MAE, MAPE, and residual diagnostics. Results show that the Fourier Series model performs substantially better, achieving lower GCV (0.3520), MSE (0.00415 training; 0.00114 testing), and MAE (0.34015 training; 0.12940 testing), as well as lower MAPE (1.26% training; 0.47% testing). In contrast, the MSAR model yields higher errors with GCV (0.5747), MSE (0.9113 training; 0.4686 testing), MAE (0.8005 training; 0.5512 testing), and MAPE (1.96% training; 1.34% testing). These results indicate that Sleman’s temperature dynamics characterized by stable oscillatory patterns with minimal regime shifts are more effectively captured through harmonic decomposition. The study reinforces the importance of periodic modeling for mixed-topography regions like Sleman and recommends future research integrating additional climatic variables, hybrid statistical–machine-learning frameworks, and longer time spans to improve responsiveness to extreme events and nonlinear atmospheric behavior.
Co-Authors Alexandra, Victoria Anggia Cahyoko, Fajar Dwi Elly Pusporani Fajrina, Sofia Andika Nur Idrus Syahzaqi Nahar, Muhammad Hafidzuddin Pratama, Fachriza Yosa Riefky, Muhammad Yuniar, Muhammad Alvito Dzaky Putra