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All Journal Media Statistika CAUCHY: Jurnal Matematika Murni dan Aplikasi Jurnal Mahasiswa Statistik Journal of Innovation and Applied Technology Jurnal Teknologi Informasi dan Ilmu Komputer Mutiara Medika: Jurnal Kedokteran dan Kesehatan Prosiding SI MaNIs (Seminar Nasional Integrasi Matematika dan Nilai-Nilai Islami) Jurnal Penelitian Pendidikan IPA (JPPIPA) JURNAL ILMIAH MATEMATIKA DAN TERAPAN BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika) ComTech: Computer, Mathematics and Engineering Applications Industri Inovatif : Jurnal Teknik Industri Pakem : Jurnal Pengabdian Kepada Masyarakat
Henny Pramoedyo
Prodi Statistika Jurusan Matematika FMIPA Universitas Brawijaya
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Journal : JTAM (Jurnal Teori dan Aplikasi Matematika)

 1 
Spatio-Temporal Median Polish Kriging with ARIMA Integration for Monthly Precipitation Interpolation in East Kalimantan Jannah, Friendtika Miftaqul; Fitriani, Rahma; Pramoedyo, Henny
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 2 (2025): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i2.29570

Abstract

Precipitation can lead to disasters like droughts and floods, necessitating accurate interpolation methods. Traditional spatio-temporal kriging often struggles with outliers, which can reduce estimation reliability. This study develops spatio-temporal median polish kriging, which separates spatial and temporal components to improve interpolation accuracy, particularly in handling outliers. Unlike conventional kriging, this method integrates median polish kriging for robust spatial interpolation and ARIMA for capturing temporal trends, making it more effective in dynamic precipitation pattern estimation. The study utilizes precipitation data from seven observation posts in East Kalimantan (2021–2023). The data is processed using a combination of spatial, temporal, and spatial-temporal modeling approaches to capture precipitation variations accurately. For spatial interpolation, the study applies kriging in median polish spatial effects. The best semivariogram model for spatial effects is exponential, which is used to characterize spatial dependencies. To capture temporal effects of median polish, the study employs ARIMA(1,2,0), which models precipitation trends over time and helps manage temporal fluctuations. For residuals of median polish interpolation, the study applies spatio-temporal kriging, using a simple sum-metric model as the best approach to integrate both spatial and temporal dependencies. The semivariograms selected for spatial, temporal, and joint dependencies follow a gaussian structure. The interpolation results reveal that precipitation increases toward the west, with precipitation patterns also showing an increasing trend over time. These findings demonstrate the model’s capability in capturing spatial and temporal precipitation variations while addressing potential outliers through the median polish approach. By utilizing a robust statistical framework, the model reduces the influence of extreme values, leading to more reliable precipitation estimates. However, this study utilizes only seven observation posts. The limited number of observation posts may introduce uncertainty in regions distant from measurement stations and affect the model's accuracy. Therefore, further research should test this model by applying it to different geographical regions with a more extensive dataset.
Modeling Spatio-Temporal Precipitation Patterns in East Kalimantan using Space-Time Kriging and Median Polish-Based Spatio-Temporal Kriging Jannah, Friendtika Miftaqul; Fitriani, Rahma; Pramoedyo, Henny
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 3 (2025): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i3.30642

Abstract

Precipitation variability presents significant challenges for disaster risk reduction and water resource management, particularly in flood and drought-prone regions such as East Kalimantan. This study aims to develop and evaluate two statistical approaches for spatio-temporal precipitation modeling: spatio-temporal kriging (ST-Kriging) and spatio-temporal median polish kriging (ST-MPK). Using monthly precipitation data obtained from seven observation stations provided by BMKG and BPS for the period 2021 to 2023, both models were assessed using performance metrics. ST-Kriging employed a simple sum-metric semivariogram model that combines exponential spatial and Gaussian temporal components. This model achieved an RMSE of 84.05, MAE of 69.95, and MAPE of 52.67%. Meanwhile, ST-MPK model, incorporating robust median polish decomposition and ST-Kriging of residuals, produced a lower MAPE of 44.83% with higher RMSE (122.44) and MAE (91.35). This suggests that while ST-Kriging offers better absolute error performance, ST-MPK provides greater relative accuracy and improved robustness to outliers, critical advantages for modeling precipitation in regions undergoing environmental shifts, where anomalies and extremes are increasingly common. These findings highlight ST-MPK’s potential to produce more reliable forecasts under irregular precipitation conditions, supporting early warning systems and informed water resource planning. Scientifically, this research contributes a robust modeling framework suitable for data-scarce and outlier-prone contexts. Practically, it can aid policymakers in designing adaptive flood mitigation strategies and sustainable water management policies tailored to the evolving climate realities of East Kalimantan.
Spatial Panel Regression Modelling of Rainfall in Indonesia Saniyawati, Fang You Dwi Ayu Shalu; Astutik, Suci; Pramoedyo, Henny
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 2 (2025): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i2.29882

Abstract

Rainfall is amount of water that falls to the earth's surface in the form of rain during a certain period of time, usually measured in millimeters. Rainfall data in Indonesia usually includes temporal and spatial dimensions, so the appropriate method for its analysis is spatial panel regression analysis. This study aims to identify factors that influence the amount of rainfall in Indonesia. This type of research is quantitative using secondary data from the central statistics agency website. The predictor variables used include air temperature, sunshine radiation, humidity, wind speed, and air pressure, while the response variable is amount of rainfall in 34 provinces in Indonesia. Spatial panel regression analysis is carried out using maximum likelihood estimation, which is used to estimate the regression coefficient and intercept that maximizes the likelihood of the existing data. Based on the lagrange multiplier test, spatial autocorrelation was found in the lag, so the appropriate model is SAR-FE. This model can overcome spatial autocorrelation by taking into account spatial interactions between locations, as well as controlling unobserved heterogeneity through fixed effects. The results show that sunshine radiation, humidity, and wind speed have significant effect on the amount of rainfall in Indonesia. The AIC value of SAR-FE model (-4.352594×〖10〗^(-13)) is smaller than SEM-FE model (-1.642001×〖10〗^(-12)), indicating that SAR-FE model is better at explaining the data.
Co-Authors Achmad Efendi Alfi Fadliana Amelia, Okky Ariska Ani Budi Astuti Ani Budi Astuti Ardianti, Deby Arif, Nur Fitriyah Atiek Iriany Chairunissa, Abela Danang Ariyanto Eni Sumarminingsih Fachri Faisal Fernandes, Adji Achmad Fernandes, Adji Achmad Rinaldo Handoyo, Samingun Heni Kusdarwati Jaka Pratama Musashi Jannah, Friendtika Miftaqul Khoirunnisa, Elsa Azizah Korniasari, Leli Dwi Kurniawan, Galih Widhi Kusdarwati, Heni Liduina Asih Primandari, Liduina Asih Loekito Adi Soehono Luthfatul Amaliana, Luthfatul Maghfiroh, Aulia Maharani, Kasih Megasari, Dannys Melanwati, Rinda Lolita Mitakda, Maria Bernadetha Mudjiono Mudjiono, Mudjiono Ni Wayan Surya Wardhani Ni Wayan Surya Wardhani Novi Nur Aini, Novi Nur Nur Azizah Nurjannah Nurjannah Rahma Fitriani Ramadhan, Apry Zakaria Ramadhan, Rajuliaddin Ridwan, Yusrina Layli Riza, Sativandi Rizkiyani, Cirairina Sa’adah, Zumrotus Saniyawati, Fang You Dwi Ayu Shalu Saris, Laode Muhammad Sariyya, Hanah Rista Septiani, Kurniawati Setiarini, An Nisa Dwi Shara, Yoeniarti Suci Astutik Sumarminingsih, Eni Widya Reza Wigbertus Ngabu Yanuari, Anindita Yuli Triana, Eka Putri