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Spatial Weighting Selection in GSTAR and S-GSTAR Models for Temperature Prediction

Jurnal Matematika, Statistika dan Komputasi · Vol. 20 No. 3 (2024) · pp. 639–653

DOI
10.20956/j.v20i3.34305
ISSN
2614-8811, 1858-1382
Published
2024-05-15
Publisher
Department of Mathematics, Hasanuddin University
Language
en
License
creativecommons.org/licenses/by/4.0

Abstract

English

Recent research in time series analysis indicates that events at a particular location are not only influenced by events at previous times but also by proximity between locations. Events influenced by both space and time can be modeled using a space-time model. GSTAR model is one such space-time model. In its development, time series data exhibiting seasonal patterns are modeled using Seasonal GSTAR (S-GSTAR). The GSTAR and S-GSTAR models are used to model temperature in the Banjar, Cilacap, and Sleman Districts. The purpose of employing both methods is to compare the best model for modeling temperature at these three locations. Spatial weights used include inverse distance weighting using the Euclidean distance formula, uniform weighting, and cross-correlation normalization weighting. Ordinary Least Squares (OLS) is the estimation method used in this study. The best model obtained is S-GSTAR with inverse distance weighting, as this model has the smallest RMSE value.

Bahasa Indonesia

Penelitian terkini dalam deret waktu menunjukkan bahwa kejadian pada suatu lokasi bukan hanya dipengaruhi kejadian pada waktu sebelumnya, tetapi juga kedekatan antarlokasi. Kejadian yang dipengaruhi oleh ruang dan waktu dapat dimodelkan dengan model ruang waktu. Contoh dari model ruang waktu adalah model GSTAR. Pada perkembangannya, untuk data ruang waktu yang memiliki pola musiman dapat dimodelkan dengan Seasonal GSTAR (S-GSTAR). Model GSTAR dan S-GSTAR digunakan untuk memodelkan temperatur di Kabupaten Banjar, Cilacap, Sleman. Tujuan penggunaan kedua metode tersebut adalah untuk membandingkan model yang terbaik dalam memodelkan temperature pada ketiga lokasi tersebut. Bobot spasial yang digunakan yaitu bobot invers jarak dengan rumus euclidian distance, bobot seragam, dan bobot normalisasi korelasi silang. OLS (Ordinary Least Square) merupakan metode estimasi yang digunakan pada penelitian ini. Model terbaik yaitu model S-GSTAR dengan bobot spasial inversi jarak, hal ini dikarenakan model tersebut nilai RMSE terkecil.

Keywords

Collaboration network of the authors

16 authors · 31 co-authorship links

Hover or tap a name to highlight its co-authors. Double-click to open the author's page.

  • Politeknik Negeri Ujung Pandang
  • Affiliation unknown
  • Different organisations
  • Same organisation
  • Affiliation unknown
  • Thicker line = more joint articles · bigger circle = more articles
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Co-authorOrganisationJoint articles
Muhammad Rozzaq HamidiAffiliation unknown3
Nurhayati NurhayatiPoliteknik Negeri Ujung Pandang2
Kurnia Novita SariAffiliation unknown2
Nur'ainul Miftahul HudaAffiliation unknown1
Nurfitri Imro'ahAffiliation unknown1
Asrul IrfanullahAffiliation unknown1
Nuraziza ArfanAffiliation unknown1
Novi MardianaAffiliation unknown1
Syifa Nurul FatimahAffiliation unknown1
Ahmad Fuad ZainnuddinAffiliation unknown1
Hamidah Qurrotun NadwahAffiliation unknown1

Affiliations come from OpenAlex; journal OAI-PMH metadata carries none. Authors without an OpenAlex ID are matched by name, which can merge or split people.

Metadata source: OAI-PMH (metadata jurnal) https://journal.unhas.ac.id/index.php/jmsk/oai, first harvested 5 Nov 2026, last seen 5 Nov 2026.
Original metadata (oai_dc) 
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	<dc:title xml:lang="en">Spatial Weighting Selection in GSTAR and S-GSTAR Models for Temperature Prediction</dc:title>
	<dc:creator xml:lang="en">Utami, Riani</dc:creator>
	<dc:creator xml:lang="en">Mukhaiyar, Utriweni </dc:creator>
	<dc:creator xml:lang="en">Mardiyah, Nabila</dc:creator>
	<dc:creator xml:lang="en">Sa’adah, Yalela </dc:creator>
	<dc:creator xml:lang="en">Widyawati, Erni</dc:creator>
	<dc:subject xml:lang="en">	Space-time</dc:subject>
	<dc:subject xml:lang="en">GSTAR</dc:subject>
	<dc:subject xml:lang="en">seasonal</dc:subject>
	<dc:subject xml:lang="en">temperature,</dc:subject>
	<dc:subject xml:lang="en">prediction</dc:subject>
	<dc:description xml:lang="en">Recent research in time series analysis indicates that events at a particular location are not only influenced by events at previous times but also by proximity between locations. Events influenced by both space and time can be modeled using a space-time model. GSTAR model is one such space-time model. In its development, time series data exhibiting seasonal patterns are modeled using Seasonal GSTAR (S-GSTAR). The GSTAR and S-GSTAR models are used to model temperature in the Banjar, Cilacap, and Sleman Districts. The purpose of employing both methods is to compare the best model for modeling temperature at these three locations. Spatial weights used include inverse distance weighting using the Euclidean distance formula, uniform weighting, and cross-correlation normalization weighting. Ordinary Least Squares (OLS) is the estimation method used in this study. The best model obtained is S-GSTAR  with inverse distance weighting, as this model has the smallest RMSE value.</dc:description>
	<dc:description xml:lang="id">Penelitian terkini dalam deret waktu menunjukkan bahwa kejadian pada suatu lokasi bukan hanya dipengaruhi kejadian pada waktu sebelumnya, tetapi juga kedekatan antarlokasi. Kejadian yang dipengaruhi oleh ruang dan waktu dapat dimodelkan dengan model ruang waktu. Contoh dari model ruang waktu adalah model GSTAR. Pada perkembangannya, untuk data ruang waktu yang memiliki pola musiman dapat dimodelkan dengan Seasonal GSTAR (S-GSTAR). Model GSTAR dan S-GSTAR digunakan untuk memodelkan temperatur di Kabupaten Banjar, Cilacap, Sleman. Tujuan penggunaan kedua metode tersebut adalah untuk membandingkan model yang terbaik dalam memodelkan temperature pada ketiga lokasi tersebut. Bobot spasial yang digunakan yaitu bobot invers jarak dengan rumus euclidian distance, bobot seragam, dan bobot normalisasi korelasi silang. OLS (Ordinary Least Square) merupakan metode estimasi yang digunakan pada penelitian ini. Model terbaik yaitu model S-GSTAR&amp;nbsp;dengan bobot spasial inversi jarak, hal ini dikarenakan model tersebut &amp;nbsp;nilai RMSE terkecil.
&amp;nbsp;</dc:description>
	<dc:publisher xml:lang="en">Department of Mathematics, Hasanuddin University</dc:publisher>
	<dc:date>2024-05-15</dc:date>
	<dc:type>info:eu-repo/semantics/article</dc:type>
	<dc:type>info:eu-repo/semantics/publishedVersion</dc:type>
	<dc:format>application/pdf</dc:format>
	<dc:identifier>https://journal.unhas.ac.id/index.php/jmsk/article/view/34305</dc:identifier>
	<dc:identifier>10.20956/j.v20i3.34305</dc:identifier>
	<dc:source xml:lang="en">Jurnal Matematika, Statistika dan Komputasi; Vol. 20 No. 3 (2024): May 2024; 639-653</dc:source>
	<dc:source>2614-8811</dc:source>
	<dc:source>1858-1382</dc:source>
	<dc:language>en</dc:language>
	<dc:relation>https://journal.unhas.ac.id/index.php/jmsk/article/view/34305/11478</dc:relation>
	<dc:relation>10.20956/j.v20i3.34305.g11478</dc:relation>
	<dc:rights xml:lang="en">Copyright (c) 2024 Author and publisher</dc:rights>
	<dc:rights xml:lang="en">https://creativecommons.org/licenses/by/4.0</dc:rights>
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