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All Journal Jurnal Matematika BIMASTER GRADIEN Jurnal Geocelebes BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika) Jurnal Pengabdian Masyarakat Bumi Raflesia Dharma Raflesia : Jurnal Ilmiah Pengembangan dan Penerapan IPTEKS Jurnal Ilmiah Matematika Jurnal Eurekamatika MATHunesa: Jurnal Ilmiah Matematika Journal of Mathematics UNP Indonesian Journal of Community Empowerment and Service Aceh International Journal of Science and Technology Proceeding International Conference on Mathematics and Learning Research Indonesian Journal of Applied Mathematics and Statistics
Jose Rizal
Department Of Mathematics, Faculty Of Mathematics And Natural Sciences, Universitas Bengkulu, Indonesia
Agriculture, Biological Sciences & Forestry Humanities Chemical Engineering, Chemistry & Bioengineering Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Earth & Planetary Sciences Economics, Econometrics & Finance Education Energy Engineering Industrial & Manufacturing Engineering Languange, Linguistic, Communication & Media Mathematics Mechanical Engineering Physics Public Health Social Sciences Transportation Other

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Comparative Analysis of ARMA and GARMA Models in Predicting the Blooming Dynamics of Rafflesia arnoldii in Bengkulu Province Amelliana Melasarrah; Jose Rizal; Winalia Agwil
Indonesian Journal of Applied Mathematics and Statistics Vol. 3 No. 1 (2026): Indonesian Journal of Applied Mathematics and Statistics (IdJAMS)
Publisher : PT Anugrah Teknologi Kecerdasan Buatan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.71385/idjams.v3i1.29

Abstract

Bengkulu Province, known as the Land of Rafflesia, is home to Rafflesia arnoldii, a rare and iconic flowering species. Understanding the temporal dynamics of its blooming frequency is essential not only for effective conservation planning but also for strengthening flora-based ecotourism initiatives. Time series forecasting has been widely applied to ecological and environmental data, with the Autoregressive Moving Average (ARMA) model being one of the most commonly used approaches. However, ARMA relies on the white-noise assumption, which is often violated in count data such as the number of Rafflesia arnoldii blooms, leading to reduced accuracy. To address this limitation, this study applies the Generalized Autoregressive Moving Average (GARMA) model, which accommodates non-Gaussian data from the exponential family, including Poisson and Negative Binomial distributions. The dataset consists of monthly records of blooming events collected by the Bengkulu Natural Resources Conservation Agency from January 2015 to December 2023. Model performance was evaluated using Root Mean Square Error (RMSE), Mean Absolute Deviation (MAD), and Mean Arctangent Absolute Percentage Error (MAAPE). Results show that GARMA(1,0) achieved RMSE = 2.424, MAD = 2.224, and MAAPE = 31%, while GARMA(0,2) achieved RMSE = 2.550, MAD = 1.483, and MAAPE = 26%. In contrast, ARMA(1,0) performed less effectively, with RMSE = 3.694, MAD = 2.676, and MAAPE = 36%. These findings demonstrate that GARMA provides more stable and accurate forecasts, effectively capturing the stochastic properties of count data without depending on residual normality. The study highlights the methodological superiority of GARMA over ARMA, offering both theoretical contributions to time series modeling and practical benefits for biodiversity conservation. By enabling more reliable predictions of Rafflesia arnoldii blooms, GARMA can inform conservation policies and support sustainable tourism strategies in Bengkulu Province.
Co-Authors , Debora Acnesya, Vivin Adi Irwanto Agwil, Winalia Amelliana Melasarrah Baki Swita Bella, Claudia Cantika Cinta Rizki Oktarina Dwi Kumala, Siska Dzakirah, Qanitahudz Etis Sunandi Fachri Faisal Faisal, Fahri Firdaus Firdaus Idhia Sriliana Lestari, Wina Ayu Natisharevi, Raditya Janaloka Nur Afandi Nurul Hidayati Pepi Novianti Pratiwi, Stevy Cahya Rafflesia, Ulfa Rahma Sholeha, Tari Ramya Rachmawati Ratna Widayati Riki Wahyudi Riri Sesiati Septa, Oon Septri Damayanti Setiawan, Aisyah Nooravieta Sigit Nugroho Sigit Nugroho Siska Yosmar Sunandi, Etis Syahrul Akbar Tasyah, Qhiky Lioni Ulfasari Rafflesia Winalia Agwil Yulian Fauzi