Modeling Spatial Autoregressive Moving Average on the Human Development Index

(Studi Kasus: Indeks Pembangunan Manusia Kabupaten/Kota di Pulau Kalimantan)

Authors

  • Ardiman Wiranata Department of Mathematics, Study Program of Statistics, Mulawarman University, Samarinda, East Kalimantan, Indonesia
  • M. Fathurahman Department of Mathematics, Faculty of Mathematics and Natural Sciences, Mulawarman University, Samarinda, East Kalimantan, Indonesia https://orcid.org/0000-0002-5993-4196
  • Rito Goejantoro Department of Mathematics, Study Program of Statistics, Mulawarman University, Samarinda, East Kalimantan, Indonesia

DOI:

https://doi.org/10.20956/j.v21i3.36392

Keywords:

spatial regression, SARMA, HDI

Abstract

The Spatial Autoregressive Moving Average (SARMA) model is a regression model developed from the classical regression model. The classical regression model produces inaccurate conclusions when used to model spatial data because the assumption of independent errors is not met. The SARMA model has advantages in modeling spatial data that has a spatial effect on the lag of the dependent variable and error. This study aims to obtain a SARMA model and factors that significantly influence the Human Development Index (HDI) of districts and cities in Kalimantan in 2022 based on the SARMA model. The spatial weighting used in SARMA modeling is rook contiguity. The results of the study show that the SARMA model can model the HDI of districts and cities in Kalimantan. The factors that significantly influence the HDI of districts and cities in Kalimantan are the poverty rate, the open unemployment rate, and the number of hospital facilities.

References

[1] Alwi, W., Jajang. & Nurhayati, N., 2019. Pemodelan Indeks Pembangunan Manusia di Provinsi Jawa Tengah Tahun 2017 Menggunakan Analisis Regresi Spasial. Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP), Vol. 11, No. 1, 45-58.

[2] Anselin, L., 1988a. Lagrange Multiplier Test Diagnostics for Spatial Dependence and Spatial Heterogeneity. Geographical Analysis, Vol. 20, No. 1, 1-17.

[3] Anselin, L., 1988b. Spatial Econometrics: Methods and Models. Kluwer Academic Publisher, Dordrecht.

[4] Cressie, N. A., 1991. Statistics for Spatial Data. John Wiley & Sons, Inc., New York.

[5] Fathurahman, M., Hayati, M. N. & Rizki, N. A., 2019. Pemodelan Indeks Pembangunan Kesehatan Masyarakat Kabupaten/Kota di Pulau Kalimantan Menggunakan Regresi Spasial. Prosiding Seminar Nasional Matematika, Statistika dan Aplikasinya 2019, 183-191, Jurusan Matematika, FMIPA Universitas Mulawarman, Samarinda.

[6] Huang, J. S., 1984. The Autoregressive Moving Average Model for Spatial Analysis. Australian Journal of Statistics, Vol. 26, No. 2, 169-178.

[7] Lispani, N. M., Sumarjaya, I. W. & Sukarsa, I. K., 2018. Pemodelan Jumlah Tindak Kriminalitas di Provinsi Jawa Timur dengan Analisis Regresi Spatial Autoregressive and Moving Average. E-Jurnal Matematika, Vol. 7, No. 4, 346-356.

[8] Nirmala, K. L., Pramesti, W. & Fitriani, F., 2022. Spatial Autoregressive Moving Average pada Pemodelan Persentase Penduduk Miskin Kabupaten/Kota di Provinsi Jawa Timur Tahun 2020. Jurnal Statistika, Vol. 15, No. 1, 158-166.

[9] Permai, S. D., Jauri, R. & Chowanda, A., 2019. Spatial Autoregressive (SAR) Model for Average Expenditure of Papua Province. Procedia Computer Science, Vol. 157, 537-542.

[10] Permana, R. S., Kismiantini. & Setiawan, E. P., 2024. Pemodelan Indeks Pembangunan Manusia di Provinsi Jawa Tengah Tahun 2022 Menggunakan Model Regresi Spasial dengan Pembobot Queen Contiguity dan K-Nearest Neighbor. Jurnal Statistika dan Sains Data, Vol. 1, No. 2, 48-64.

[11] Rosa, M., Maiyastri & Yozza, H., 2020. Pemodelan Indeks Pembangunan Manusia Menggunakan Analisis Regresi Spasial di Provinsi Jawa Timur. Jurnal Matematika UNAND, Vol. 9, No. 4, 347-356.

[12] Sari, D. N., Hayati, M. N. & Wahyuningsih, S., 2020. Model Spatial Autoregressive Moving Average (SARMA) pada Data Jumlah Kejadian Demam Berdarah Dengue (DBD) di Provinsi Kalimantan Timur dan Tengah Tahun 2016. Jurnal Eksponensial, Vol. 11, No. 1, 57-64.

[13] Tan, C. & Elhorst, J. P., 2024. The Spatial Autoregressive Panel Data Model with Spatial Moving Average Errors. Geographical Analysis,Vol. 56, 40-61.

[14] Wardani, I. K., Handajani, S. S. & Zukhronah, E., 2019. Pemodelan Tingkat Pengangguran Terbuka Provinsi Jawa Tengah Menggunakan Model Spatial Autoregressive Moving Average. Prosiding Sendika 2019, 199-205. Department of Mathematics Education, Universitas Muhammadiyah, Purworejo.

[15] Widyastuti, M. N., Srinadi, I. G. & Susilawati, M., 2019. Pemodelan Jumlah Kasus Pneumonia Balita di Jawa Timur Menggunakan Regresi Spatial Autoregressive Moving Average. E-Jurnal Matematika, Vol. 8, No. 3, 236-245.

[16] Yulianto, S., Utami, A. Z. & Ambarwati, A. N., 2024. Perbandingan Model Spasial dalam Permasalahan Kemiskinan di Provinsi Jawa Timur. Statistika, Vol. 24, No. 2, 143-150.

Downloads

Published

2025-05-14

How to Cite

Wiranata, A., Fathurahman, M., & Goejantoro, R. (2025). Modeling Spatial Autoregressive Moving Average on the Human Development Index: (Studi Kasus: Indeks Pembangunan Manusia Kabupaten/Kota di Pulau Kalimantan). Jurnal Matematika, Statistika Dan Komputasi, 21(3), 646–654. https://doi.org/10.20956/j.v21i3.36392

Issue

Vol. 21 No. 3 (2025): MAY 2025

Section

Research Articles

License

Copyright (c) 2025 Jurnal Matematika, Statistika dan Komputasi

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Jurnal Matematika, Statistika dan Komputasi is an Open Access journal, all articles are distributed under the terms of the Creative Commons Attribution License, allowing third parties to copy and redistribute the material in any medium or format, transform, and build upon the material, provided the original work is properly cited and states its license.  This license allows authors and readers to use all articles, data sets, graphics and appendices in data mining applications, search engines, web sites, blogs and other platforms by providing appropriate reference.