Does Bitcoin hedge trade policy uncertainty shocks? horizon- and state-dependent evidence from wavelet and quantile regressions

We investigate whether Bitcoin hedges trade policy uncertainty (TPU) shocks across different investment horizons. A TPU shock is defined as a day when the TPU index exceeds its 95th percentile. We combine wavelet decomposition with quantile regression, quantile-in-quantile (QQ) regression, and rolling quantile regression to examine how Bitcoin responds across return states and time scales. For investors, a positive total TPU effect means Bitcoin returns rise as trade policy uncertainty increases during shock periods, which is consistent with hedging behaviour. A negative effect means Bitcoin moves adversely with the shock and offers little protection. The standard quantile regressions produce effects that are mostly close to zero, indicating weak average hedging ability. The QQ estimates reveal stronger differences across horizons and market states. Short-horizon effects frequently change sign, while medium-horizon are largely negative. The long-run component becomes positive over parts of the middle and upper return distribution but remains negative in the lower tail. Rolling estimates at the 10th and 90th quantiles are also generally close to zero and statistically weak. Generally, Bitcoin does not provide a stable hedge against TPU shocks; any protection is conditional on market state and investment horizon.