Bitcoin, Gold, and Stock Market Volatility Including COVID-19 Periods: Comparative Analysis Using GARCH and DCC-MGARCH Models

Abstract

This study investigates the volatility dynamics and time-varying correlations between Bitcoin (BTC) and major financial and commodity markets, including gold, oil, NASDAQ, NIKKEI, FTSE, DAX, and the U.S. Dollar Index (USDINX). Using daily data and GARCH-family models, we quantify persistence, asymmetry, and mediumterm memory in BTC volatility. Model selection using loglikelihood, SIC, and AIC criteria identifies EGARCH asthe best model for capturing conditional variance behavior. We then employ a DCC-MGARCH framework to estimate evolving cross-market correlations. Results indicate that BTC volatility is highly persistent, exhibits stronger reactions to negative shocks, and shows moderate mean reversion. Gold displays the lowest persistence, confirming its role as a stable diversifier. DCC-MGARCH estimates reveal weak positive BTC-Gold correlations, negative BTC-USDINX correlations, and no significant BTC-Oil or BTC-DAX linkages, implying substantial diversification potential. Notably, BTC-NIKKEI correlations strengthened during the COVID-19 period, while BTC-Gold correlations modestly increased. These findings underscore the importance of dynamic portfolio strategies, as optimal weights shift in response to evolving conditional covariances, rendering static allocations suboptimal. For policymakers, volatility persistence and correlation thresholds can inform leverage and exposure limits, particularly when the linkages between BTC and traditional assets intensify.