Bitcoin Transaction Multivariate Forecasting Analysis Deep Learning Model Walk Forward Validation

Abstract

The volatile and non-linear movement of Bitcoin prices makes price prediction a complex problem in time series analysis. This study aims to compare the performance of several deep learning models, namely Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU), Transformer, and Temporal Fusion Transformer (TFT), in predicting Bitcoin closing prices based on multivariate data. The dataset consists of daily historical data from 2020 to 2025, including Open, High, Low, Close, and Volume features. Model evaluation was conducted using the Walk Forward Validation (WFV) approach with 5 folds and was compared with the Cross Validation (CV) method. Three data split scenarios were applied: 70:30, 80:20, and 90:10. Model performance was measured using Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), Mean Absolute Percentage Error (MAPE), Symmetric MAPE (sMAPE), and the coefficient of determination (R²). Furthermore, the Wilcoxon Signed-Rank Test was employed to analyze the statistical significance of performance differences between validation methods. The results indicate that the GRU model under the 90:10 data split scenario achieved the best performance, with a median MAE of 0.0116 and RMSE of 0.0179, along with an R² value of 0.8622. This model demonstrated lower prediction errors and greater stability compared to the other models. Meanwhile, the Wilcoxon test results showed no significant difference between Walk Forward Validation and Cross Validation (p-value > 0.05), indicating that both validation methods produce statistically equivalent performance. Based on these findings, the GRU model is recommended as the most optimal model for Bitcoin price prediction under the experimental configuration used in this study.