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Comparison of hybrid models VMD-LSTM and VMD-RNN for monthly forecasting of international tourist arrivals in Indonesia by entry point

Statistical Modeling and Data Science · Vol. 1 No. 1 (2026) · pp. 1–21

DOI
10.15294/smds.v1i1.50228
Published
2026-09-09
Publisher
Universitas Negeri Semarang
Language
eng

Abstract

Accurate forecasting of international tourist arrivals is crucial for strategic planning, but the nonlinear and volatile nature of tourism data presents significant modeling challenges. This study evaluates the effectiveness of a hybrid decompose and ensemble approach for estimating international tourist arrivals to Indonesia via three main entry points: air, sea, and land. Unlike traditional frequency component decomposition methods, the proposed hybrid model Variational Mode Decomposition-Long Short Term Memory (VMD-LSTM) and Variational Mode Decomposition-Recurrent Neural Network (VMD-RNN) integrates all Intrinsic Mode Functions (IMFs) resulting from Variational Mode Decomposition (VMD) into a single multivariate dataset to project all components simultaneously. These models were evaluated using monthly time-series data from January 2008 to March 2026. Contrary to the common assumption that decomposition always improves accuracy, this study demonstrates the theoretical duality of high-order multivariate decomposition (K=12) based on data volatility. For the air route, standalone LSTM delivered the most robust generalization without decomposition (test R2 = 96.48%), while hybrid configurations suffered degradation attributable to the accumulation of reconstruction error variance during the linear combination of the 12 IMF components. On the sea route the effect was architecture-dependent: standalone RNN (R2 = 86.90%) and VMD-RNN (R2 = 91.69%) both generalized well, whereas VMD-LSTM underperformed (R2 = 84.83%). Conversely, on the purely chaotic and noise-laden land route, the multivariate hybrid models (VMD-RNN and VMD-LSTM) successfully reversed this behavior, outperforming their single counterparts by achieving test R2 scores of 76.18% and 75.93% compared to only 51.96% for RNN and 36.94% for LSTM. This study concludes that high-order decomposition acts as a reliable noise filter in volatile environments but becomes a source of error variance inflation in stable data streams.

Keywords

Collaboration network of the authors

40 authors · 73 co-authorship links · 2 across different organisations · showing the 40 most connected

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

  • State University of Semarang
  • Universitas Halu Oleo
  • Universitas Airlangga
  • Affiliation unknown
  • Different organisations
  • Same organisation
  • Affiliation unknown
  • Thicker line = more joint articles · bigger circle = more articles
Show as table
Co-authorOrganisationJoint articles
Zaenuri ZaenuriState University of Semarang3
Fajar Sodik PamungkasAffiliation unknown3
Dedy KurniantoAffiliation unknown3
St. Budi WaluyaAffiliation unknown2
Jannatun Khustia LubisAffiliation unknown2
Alif Aulia RahmanAffiliation unknown2
Mohammad AsikinAffiliation unknown2
Muhammad AshimAffiliation unknown2
Nur HasanahUniversitas Halu Oleo2
Rohimatul AzizahAffiliation unknown2
Bayu Dwi PrasetyaAffiliation unknown2
Fatkhurokhman FauziAffiliation unknown2
MulyonoAffiliation unknown1
Noviana Dini RahmawatiAffiliation unknown1
Mira Dwi UtamiAffiliation unknown1
Nike Yustina OktavianiAffiliation unknown1
Luthfiyah AstutiningtyasAffiliation unknown1
Riska Nur FitrianingsihAffiliation unknown1
Annisa IkrimahAffiliation unknown1
Supriyono SupriyonoAffiliation unknown1
Mohammad Jefrie Ilham AkbarAffiliation unknown1
Faris Febri RahantoAffiliation unknown1
Muhammad Nurul MuttaqinAffiliation unknown1
Iwan JunaediState University of Semarang1
Sanianajiba Nugroho PutriAffiliation unknown1
Hendrik SutrisnoAffiliation unknown1
Yeni NurochmahAffiliation unknown1
WardonoAffiliation unknown1
MunaAffiliation unknown1
Tri Sri Noor AsihAffiliation unknown1
Rizki Ahid NurhasanahAffiliation unknown1
Petronela Ivoni SusantyAffiliation unknown1
Kartono KartonoUniversitas Airlangga1
Luluk Ulfa ChasaniAffiliation unknown1
Tri Sri Noor AsihAffiliation unknown1
Wardono WardonoAffiliation unknown1
Nurlaela Eka CahyatiAffiliation 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.unnes.ac.id/journals/smds/oai, first harvested 6 Nov 2026, last seen 8 Nov 2026.
Original metadata (oai_dc) 
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	<dc:title xml:lang="en">Comparison of hybrid models VMD-LSTM and VMD-RNN for monthly forecasting of international tourist arrivals in Indonesia by entry point</dc:title>
	<dc:creator xml:lang="en">Akmalina, Alfina</dc:creator>
	<dc:creator xml:lang="en">Astuti, Elya Gita</dc:creator>
	<dc:creator xml:lang="en">Kharisudin, Iqbal</dc:creator>
	<dc:subject xml:lang="en">Deep Learning</dc:subject>
	<dc:subject xml:lang="en">Recurrent Neural Network</dc:subject>
	<dc:subject xml:lang="en">Time Series Modeling</dc:subject>
	<dc:subject xml:lang="en">Tourism Forecasting</dc:subject>
	<dc:subject xml:lang="en">Variational Mode Decomposition</dc:subject>
	<dc:description xml:lang="en">Accurate forecasting of international tourist arrivals is crucial for strategic planning, but the nonlinear and volatile nature of tourism data presents significant modeling challenges. This study evaluates the effectiveness of a hybrid decompose and ensemble approach for estimating international tourist arrivals to Indonesia via three main entry points: air, sea, and land. Unlike traditional frequency component decomposition methods, the proposed hybrid model Variational Mode Decomposition-Long Short Term Memory (VMD-LSTM) and Variational Mode Decomposition-Recurrent Neural Network (VMD-RNN) integrates all Intrinsic Mode Functions (IMFs) resulting from Variational Mode Decomposition (VMD) into a single multivariate dataset to project all components simultaneously. These models were evaluated using monthly time-series data from January 2008 to March 2026. Contrary to the common assumption that decomposition always improves accuracy, this study demonstrates the theoretical duality of high-order multivariate decomposition (K=12) based on data volatility. For the air route, standalone LSTM delivered the most robust generalization without decomposition (test R2 = 96.48%), while hybrid configurations suffered degradation attributable to the accumulation of reconstruction error variance during the linear combination of the 12 IMF components. On the sea route the effect was architecture-dependent: standalone RNN (R2 = 86.90%) and VMD-RNN (R2 = 91.69%) both generalized well, whereas VMD-LSTM underperformed (R2 = 84.83%). Conversely, on the purely chaotic and noise-laden land route, the multivariate hybrid models (VMD-RNN and VMD-LSTM) successfully reversed this behavior, outperforming their single counterparts by achieving test R2 scores of 76.18% and 75.93% compared to only 51.96% for RNN and 36.94% for LSTM. This study concludes that high-order decomposition acts as a reliable noise filter in volatile environments but becomes a source of error variance inflation in stable data streams.</dc:description>
	<dc:publisher xml:lang="en">Universitas Negeri Semarang</dc:publisher>
	<dc:date>2026-09-09</dc:date>
	<dc:type>info:eu-repo/semantics/article</dc:type>
	<dc:type>info:eu-repo/semantics/publishedVersion</dc:type>
	<dc:type xml:lang="en">Peer-reviewed Article</dc:type>
	<dc:format>application/pdf</dc:format>
	<dc:identifier>https://journal.unnes.ac.id/journals/smds/article/view/50228</dc:identifier>
	<dc:identifier>10.15294/smds.v1i1.50228</dc:identifier>
	<dc:source xml:lang="en">Statistical Modeling and Data Science; Vol. 1 No. 1 (2026): September 2026; 1-21</dc:source>
	<dc:source>10.15294/smds.v1i1</dc:source>
	<dc:language>eng</dc:language>
	<dc:relation>https://journal.unnes.ac.id/journals/smds/article/view/50228/11368</dc:relation>
	<dc:rights xml:lang="en">Copyright (c) 2026 Statistical Modeling and Data Science</dc:rights>
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