Bitcoin and Gold Causality Across Quantiles, Frequencies, and Market Regimes

This study investigates directional causality between Bitcoin and gold across different market conditions. Rather than relying on mean-based dependence, we examine how causal effects vary across return quantiles, investment horizons, and market regimes. To address this question, we apply a Causal–Frequency–Quantile–Regime (CFQR) framework. The approach combines frequency-domain Granger causality, quantile-based non-causality tests, and endogenous regime classification within a unified setting. Macroeconomic controls are included to reduce omitted variable bias. Statistical inference relies on bootstrap procedures with false discovery rate correction to account for multiple testing. Using daily data from 2013 to 2025, we find that the full-sample directional dominance between Bitcoin and gold is generally weak after multiple testing adjustments. However, under stress regimes, the causal relationship of gold to Bitcoin becomes more pronounced at longer investment horizons. Under normal conditions, causal effects remain unstable and fragmented. Economic effects are modest. Variance-based hedging gains are limited, while downside risk measures show moderate improvement during stress periods. Overall, the evidence suggests that gold does not serve as a universal hedge for Bitcoin, but may exert conditional informational influence during high-uncertainty states. The CFQR framework provides a structured way to identify such state-dependent causal patterns.