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

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.