Comparative Analysis of ARMA and GARMA Models in Predicting the Blooming Dynamics of Rafflesia arnoldii in Bengkulu Province

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.