Comparing Volatility and Neural Network Models for Forecasting Bitcoin Prices in Indonesian Rupiah

Raihan Akbar (Applied Mathematics, IPB University, Bogor Regency, Indonesia)
I Wayan Mangku (Mathematics, IPB University, Bogor Regency, Indonesia)
Bib Paruhum Silalahi (Mathematics, IPB University, Bogor Regency, Indonesia)

Zero : Jurnal Sains, Matematika, dan Terapan
Vol 10, No 2 (2026): Zero: Jurnal Sains Matematika dan Terapan

As Indonesia emerges among Southeast Asia's largest cryptocurrency markets, forecasting Bitcoin priced in rupiah (BTC/IDR) has gained practical relevance, yet most research focuses on BTC/USD and overlooks domestic macroeconomic conditions. This study tests whether augmenting an Exponential GARCH with Exogenous Variables (eGARCH-X) model with a Nonlinear Autoregressive network with eXogenous inputs (NARX) improves forecasts of weekly BTC/IDR log returns, using IHSG, USD/IDR, gold price, and BI rate as exogenous inputs. Using 437 weekly observations from January 2018 to June 2026, the hybrid was benchmarked against eGARCH-X, NARX, and a restricted eGARCH without exogenous terms across three splits, evaluated with RMSE, MAE, directional accuracy, and the Diebold­­­­ Mariano test, with each network comparison replicated over ten random initializations. The eGARCH identified a well-determined conditional variance process: volatility was highly persistent (0.976), responded asymmetrically to the sign of innovations (0.038, p = 0.010), and displayed heavy tails, with standardized residuals passing all diagnostics. No model differed significantly from the eGARCH-X benchmark, directional accuracy was indistinguishable from chance throughout (43.7–55.5%), and the exogenous regressors were insignificant both inSeaksample and out-of-sample. Weekly BTC/IDR returns thus appear tractable in their variance but close to unforecastable in their conditional mean, locating the practical value of these models in volatility estimation rather than directional prediction.