Analysis of the Volatility of Bitcoin Returns as a Digital Asset Using the ARCH-GARCH Model

Abstract

Bitcoin is a digital asset with a high level of volatility, making it important to analyze using volatility models. This study aims to analyze the volatility of Bitcoin returns using the ARCH-GARCH model during the period January 2020 to April 2026. The data used are daily closing prices of Bitcoin (BTC-USD) obtained from Yahoo Finance and processed using RStudio. The analytical methods employed include descriptive statistical analysis, stationarity testing, ARIMA modeling, ARCH effect testing, and volatility modeling using ARCH-GARCH. The results show that Bitcoin price data are non-stationary, while Bitcoin return data become stationary after return transformation. Based on model selection using the AIC criterion, the best ARIMA model obtained is ARIMA(1,0,1). Residual testing indicates the presence of ARCH effects, therefore GARCH modeling is applied. From the comparison of several GARCH models, GARCH(1,1) is selected as the best model with an AIC value of -4.161214. The analysis also indicates that Bitcoin return volatility is persistent, with a value of α₁ + β₁ equal to 0.978169. In addition, forecasting results show that Bitcoin volatility is expected to remain high in future periods, indicating that Bitcoin is a digital asset with a high level of investment risk.