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All Journal Zero : Jurnal Sains, Matematika, dan Terapan
Retno Budiarti
School of Data Science, Mathematics, and Informatics, IPB University, Bogor, Indonesia
Agriculture, Biological Sciences & Forestry Chemistry Mathematics Physics

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Rainfall Risk Modelling for Rice Farming Using Continuous Hidden Markov Models David Vijanarco Martal; Berlian Setiawaty; Retno Budiarti
ZERO: Jurnal Sains, Matematika dan Terapan Vol 9, No 3 (2025): Zero: Jurnal Sains Matematika dan Terapan
Publisher : UIN Sumatera Utara

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30829/zero.v9i3.25443

Abstract

Climate change has increased rainfall variability and unpredictability, significantly impacted agricultural productivity, and raised the risk of crop failure, particularly in rain-fed rice farming systems. This study models rainfall data from Tabanan, Bali, using a continuous-time Hidden Markov Model (HMM) to identify latent weather states and assess the associated risk of rice crop failure. The model assumes four hidden states, each generating rainfall observations following a Gamma distribution. Simulation results produced Mean Absolute Percentage Error (MAPE) values below 5% for training and testing sets, indicating strong model performance in replicating rainfall patterns. Risk analysis compared simulated rainfall with rice crop water requirements across three planting periods. The second planting period (July-October) exhibited the highest risk at 3.75%. Compared to other predictive models, HMM offers superior capability in capturing temporal rainfall structure and identifying critical transition phases, making it highly suitable for agricultural risk assessment and climate-adaptive planning.
Sector-Adjusted R-vine Copula (RVMS) Extension of CAPM for Portfolio Risk Optimization Wa Ode Intan Fully Nadya; Retno Budiarti; I Gusti Putu Purnaba
ZERO: Jurnal Sains, Matematika dan Terapan Vol 10, No 2 (2026): Zero: Jurnal Sains Matematika dan Terapan
Publisher : UIN Sumatera Utara

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30829/zero.v10i2.28837

Abstract

This study evaluated the R-vine Market Sector (RVMS) model, a sector-adjusted extension of the Capital Asset Pricing Model (CAPM), for portfolio risk optimization in the Indonesian stock market using 978 daily observations from 2021 to 2025. Returns were modeled using ARMA–GARCH and R-vine copulas, and portfolios were optimized under a minimum tail-risk criterion with rolling-window backtesting. The results indicated asymmetric and tail dependence, with sectoral effects contributing substantially to portfolio risk. RVMS reduced expected tail losses by approximately 12–16% relative to CAPM at standard confidence levels, although both models showed limited performance under extreme tail conditions. Economically, RVMS provided modest improvements in risk-adjusted performance and lower drawdowns, despite higher turnover. Overall, incorporating sectoral dependence improved portfolio risk modeling, although the benefits remained moderate and context-dependent.
Co-Authors Berlian Setiawaty David Vijanarco Martal I Gusti Putu Purnaba Wa Ode Intan Fully Nadya