Bitcoin vs. the US Dollar: Unveiling Resilience Through Wavelet Analysis of Price Dynamics

This paper investigates Bitcoin’s resilience against the U.S. dollar—widely recognized as the global reserve currency—by applying a multi-method wavelet analysis framework to daily price data of Bitcoin, the USD strength index (DXY), the euro, and other assets ranging from August 2015 to June 2024. Quantitative measures—particularly the Frobenius norm of wavelet coherence and an exponential decay phase-weighting scheme—reveal that Bitcoin’s out-of-phase relationship with the dollar is lower and more sporadic than that of mainstream assets, indicating it is not tightly governed by dollar fluctuations. Even after controlling for the euro’s dominant influence in the DXY, BTC continues to show weaker coupling than mainstream assets—reinforcing the idea that it may serve as a partial hedge against dollar-driven volatility. These results support the hypothesis that Bitcoin may serve as a resilient store of value and hedge against dollar-driven market volatility, placing Bitcoin within the broader debate on global monetary frameworks. As global monetary conditions evolve, the resilience of Bitcoin (BTC) relative to the world’s leading reserve currency—the U.S. dollar—has significant implications for both investors and policymakers.