The Power of Interpolation Effects on SARIMA and LSTM: An Indonesia Domestic Forecasting Case Study

Abstract

In regional economic planning, the accurate prediction of domestic tourism demand presents a critical challenge because limited access to historical time series data often causes advanced forecasting models to perform poorly. This study aims to demonstrate how linear interpolation can effectively serve as a data augmentation technique to overcome data scarcity when developing Long Short Term Memory (LSTM) networks to forecast domestic tourism arrivals. The methodology involves evaluating four distinct forecasting models using 80 months of Indonesian domestic tourism visitation data spanning from January 2019 to August 2025. These models include a statistical benchmark SARIMA (2,0,1)(0,1,1)[3] model selected via grid search out of 216 combinations and three LSTM variants run with identical random seeds. Performance evaluation is rigorously completed using MAE, RMSE, MAPE, sMAPE, and Theil’s U statistics. Key findings reveal that while unaugmented LSTM models perform poorly relative to a simple average baseline (Theil’s U = 1.38, MAPE = 24.6%), LSTMs enhanced with triple linear interpolation achieve superior predictive accuracy (MAPE = 2.6%, sMAPE = 2.6%, Theil’s U = 0.14). This approach significantly outperforms the benchmark SARIMA model (MAPE = 8.0%, Theil’s U = 0.63), which otherwise demonstrated adequate statistical validity through satisfactory residual diagnostics, including Ljung Box and Shapiro Wilk tests. In conclusion, the study demonstrates that utilizing linear interpolation as an augmentation technique is highly appropriate and effective, enabling deep learning models like LSTMs to accurately capture underlying temporal patterns from limited tourist arrival.