Bitcoin’s Impact on Gold Price Volatility: Evidence from ARMA-GARCH Models

With the continuous development of digital assets in the global financial system, whether Bitcoin affects the price volatility of traditional safe-haven asset gold has become a new topic worth exploring. Based on the daily data from 2018 to 2024, this paper constructs ARMA-GARCH and GARCH-X models to study the explanatory power of Bitcoin yield on gold volatility. Initially, we establish data stationarity using Augmented Dickey-Fuller tests, and introduces the Bitcoin yield on the basis of the ARMA-GARCH model, and establishes an extended model for empirical analysis. It is found that Bitcoin variables are statistically significant in the GARCH-X model, and can improve the fitting effect of the model to a certain extent. Further grouping regression shows that Bitcoin has a more stable explanatory power for gold volatility in normal market conditions, while its predictive power is weakened during periods of high uncertainty. In addition, the results of the Granger causality test also show that Bitcoin has a forward predictive effect on gold yield. This paper expands the theoretical framework of gold price modeling and provides an empirical reference for investors when allocating new and traditional asset portfolios.