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Linearized Ridge Regression Modeling with MM-Estimator in Statistical Downscalling for Rainfall Forecasting

Jurnal Matematika, Statistika dan Komputasi · Vol. 21 No. 3 (2025) · pp. 796–812

DOI
10.20956/j.v21i3.43203
ISSN
2614-8811, 1858-1382
Published
2025-05-14
Publisher
Department of Mathematics, Hasanuddin University
Language
en
License
creativecommons.org/licenses/by/4.0

Abstract

Rainfall is one of the important climate variables to be predicted because it affects various sectors, such as agriculture, health, and disasters. One method that can be used to forecast rainfall is statistical downscaling, which is the process of relating large-scale climate variables to local-scale climate variables. However, this method has several challenges, such as the presence of heteroscedasticity, multicollinearity, and outliers in the data. To overcome these challenges, this study proposes linearized ridge regression modelling with MM-estimator in statistical downscaling for rainfall forecasting. Linearized ridge regression is a linear regression method that can reduce the influence of multicollinearity by adding a penalty parameter to the covariance matrix. MM-estimator is a robust method that can handle outliers by using two estimators, namely the initial estimator (S-estimator) and the final estimator (M-estimator). This research uses daily rainfall data from BMKG Pangkep station and Global Circulation Model (GCM) output data as predictors. The results showed that linearized ridge regression modelling with MM-estimator has better performance than linearized ridge regression modelling without MM-estimator in terms of accuracy and resilience to outliers with a correlation value of 0.94 against the acute rainfall data, the Root Means Square Error value obtained is 97.26 and 86.57% of determinant coefisient value. Therefore, linearized ridge regression modelling with MM-estimator can be used as an alternative statistical downscaling method for rainfall forecasting. Based on the forecasting results for January - December 2023, it shows that the highest rainfall in Pangkep Regency is in January and the lowest rainfall is in September.

Keywords

Collaboration network of the authors

40 authors · 125 co-authorship links · showing the 40 most connected

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

  • Padjadjaran University
  • Sultan Ageng Tirtayasa University
  • Universitas Halu Oleo
  • Affiliation unknown
  • Different organisations
  • Same organisation
  • Affiliation unknown
  • Thicker line = more joint articles · bigger circle = more articles
Show as table
Co-authorOrganisationJoint articles
Andi M Alfin BasoAffiliation unknown4
Sri Astuti ThamrinAffiliation unknown3
Anna IslamiyatiAffiliation unknown3
Andi Kresna JayaAffiliation unknown3
Nirwan IlyasAffiliation unknown3
Andi Isna YunitaAffiliation unknown3
Raupong RaupongAffiliation unknown3
Nasrah SirajangAffiliation unknown3
Georgina Maria TinungkiAffiliation unknown3
Muhammad FadilAffiliation unknown3
Erna Tri HerdianiAffiliation unknown2
La Podje TalangkoAffiliation unknown2
Vika Yugi KurniawanAffiliation unknown2
Nurtiti SunusiAffiliation unknown2
Ade Safira SeptianyAffiliation unknown2
Anisa AnisaSultan Ageng Tirtayasa University2
Budi AyuningsihPadjadjaran University1
Iman HernamanPadjadjaran University1
Tidi DhalikaPadjadjaran University1
Destu Putra RosmawanAffiliation unknown1
Dedi RahmatPadjadjaran University1
Ansharullah AnsharullahUniversitas Halu Oleo1
Abdu Rahman BacoAffiliation unknown1
Alfiana AntohAffiliation unknown1
Yundy HafizriandaAffiliation unknown1
Rizki AdiputraAffiliation unknown1
Risma RismaAffiliation unknown1
Dewi Santika Upa P.Affiliation unknown1
Ririn AriantiAffiliation unknown1
Muhammad IdmanAffiliation unknown1
Fitri AnnisaAffiliation unknown1
Fitri FitriAffiliation unknown1
Nurkamalia NurkamaliaAffiliation unknown1
Mukrimin AdamAffiliation unknown1
Anisa Haura Salsa Fatih YusufAffiliation 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">Linearized Ridge Regression Modeling with MM-Estimator in Statistical Downscalling for Rainfall Forecasting</dc:title>
	<dc:creator xml:lang="en">SISWANTO, SISWANTO</dc:creator>
	<dc:creator xml:lang="en">Gozhi, M. Zaky Hisyam</dc:creator>
	<dc:creator xml:lang="en">Taufik, Muh. Ikbal</dc:creator>
	<dc:creator xml:lang="en">Kalondeng, Anisa</dc:creator>
	<dc:creator xml:lang="en">Sahriman, Sitti</dc:creator>
	<dc:subject xml:lang="en">Linearized Ridge Regression</dc:subject>
	<dc:subject xml:lang="en">MM-Estimator</dc:subject>
	<dc:subject xml:lang="en">Rainfall</dc:subject>
	<dc:subject xml:lang="en">Statistical Downscaling</dc:subject>
	<dc:description xml:lang="en">Rainfall is one of the important climate variables to be predicted because it affects various sectors, such as agriculture, health, and disasters. One method that can be used to forecast rainfall is statistical downscaling, which is the process of relating large-scale climate variables to local-scale climate variables. However, this method has several challenges, such as the presence of heteroscedasticity, multicollinearity, and outliers in the data. To overcome these challenges, this study proposes linearized ridge regression modelling with MM-estimator in statistical downscaling for rainfall forecasting. Linearized ridge regression is a linear regression method that can reduce the influence of multicollinearity by adding a penalty parameter to the covariance matrix. MM-estimator is a robust method that can handle outliers by using two estimators, namely the initial estimator (S-estimator) and the final estimator (M-estimator). This research uses daily rainfall data from BMKG Pangkep station and Global Circulation Model (GCM) output data as predictors. The results showed that linearized ridge regression modelling with MM-estimator has better performance than linearized ridge regression modelling without MM-estimator in terms of accuracy and resilience to outliers with a correlation value of 0.94 against the acute rainfall data, the Root Means Square Error value obtained is 97.26 and 86.57% of determinant coefisient value. Therefore, linearized ridge regression modelling with MM-estimator can be used as an alternative statistical downscaling method for rainfall forecasting. Based on the forecasting results for January - December 2023, it shows that the highest rainfall in Pangkep Regency is in January and the lowest rainfall is in September.</dc:description>
	<dc:publisher xml:lang="en">Department of Mathematics, Hasanuddin University</dc:publisher>
	<dc:date>2025-05-14</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/43203</dc:identifier>
	<dc:identifier>10.20956/j.v21i3.43203</dc:identifier>
	<dc:source xml:lang="en">Jurnal Matematika, Statistika dan Komputasi; Vol. 21 No. 3 (2025): MAY 2025; 796-812</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/43203/12808</dc:relation>
	<dc:rights xml:lang="en">Copyright (c) 2025 Jurnal Matematika, Statistika dan Komputasi</dc:rights>
	<dc:rights xml:lang="en">https://creativecommons.org/licenses/by/4.0</dc:rights>
</oai_dc:dc>