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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) · hlm. 1–21

DOI
10.15294/smds.v1i1.50228
Terbit
2026-09-09
Penerbit
Universitas Negeri Semarang
Bahasa
eng

Abstrak

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.

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  • State University of Semarang
  • Universitas Halu Oleo
  • Universitas Airlangga
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Tampilkan sebagai tabel
Rekan penulisOrganisasiArtikel bersama
Zaenuri ZaenuriState University of Semarang3
Fajar Sodik PamungkasAfiliasi tidak diketahui3
Dedy KurniantoAfiliasi tidak diketahui3
St. Budi WaluyaAfiliasi tidak diketahui2
Jannatun Khustia LubisAfiliasi tidak diketahui2
Alif Aulia RahmanAfiliasi tidak diketahui2
Mohammad AsikinAfiliasi tidak diketahui2
Muhammad AshimAfiliasi tidak diketahui2
Nur HasanahUniversitas Halu Oleo2
Rohimatul AzizahAfiliasi tidak diketahui2
Bayu Dwi PrasetyaAfiliasi tidak diketahui2
Fatkhurokhman FauziAfiliasi tidak diketahui2
MulyonoAfiliasi tidak diketahui1
Noviana Dini RahmawatiAfiliasi tidak diketahui1
Mira Dwi UtamiAfiliasi tidak diketahui1
Nike Yustina OktavianiAfiliasi tidak diketahui1
Luthfiyah AstutiningtyasAfiliasi tidak diketahui1
Riska Nur FitrianingsihAfiliasi tidak diketahui1
Annisa IkrimahAfiliasi tidak diketahui1
Supriyono SupriyonoAfiliasi tidak diketahui1
Mohammad Jefrie Ilham AkbarAfiliasi tidak diketahui1
Faris Febri RahantoAfiliasi tidak diketahui1
Muhammad Nurul MuttaqinAfiliasi tidak diketahui1
Iwan JunaediState University of Semarang1
Sanianajiba Nugroho PutriAfiliasi tidak diketahui1
Hendrik SutrisnoAfiliasi tidak diketahui1
Yeni NurochmahAfiliasi tidak diketahui1
WardonoAfiliasi tidak diketahui1
MunaAfiliasi tidak diketahui1
Tri Sri Noor AsihAfiliasi tidak diketahui1
Rizki Ahid NurhasanahAfiliasi tidak diketahui1
Petronela Ivoni SusantyAfiliasi tidak diketahui1
Kartono KartonoUniversitas Airlangga1
Luluk Ulfa ChasaniAfiliasi tidak diketahui1
Tri Sri Noor AsihAfiliasi tidak diketahui1
Wardono WardonoAfiliasi tidak diketahui1
Nurlaela Eka CahyatiAfiliasi tidak diketahui1

Afiliasi berasal dari OpenAlex; metadata OAI-PMH jurnal tidak memuatnya. Penulis tanpa ID OpenAlex dicocokkan berdasarkan nama, sehingga dua orang bisa tergabung atau satu orang bisa terpisah.

Sumber metadata: OAI-PMH (metadata jurnal) https://journal.unnes.ac.id/journals/smds/oai, pertama di-harvest 6 Nov 2026, terakhir terlihat 8 Nov 2026.
Metadata asli (oai_dc) 
<oai_dc:dc xmlns="http://www.openarchives.org/OAI/2.0/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:oai_dc="http://www.openarchives.org/OAI/2.0/oai_dc/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/oai_dc/  http://www.openarchives.org/OAI/2.0/oai_dc.xsd">
	<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>
</oai_dc:dc>