This paper develops statistical tools for testing conditional independence among the jump components ofthe daily quadratic variation, which we estimate using intraday data. To avoid sequential bias distortion, wedo not pretest for the presence of jumps. If the null is true, our test statistic based on daily integrated jumpsweakly converges to a Gaussian random variable if both assets have jumps. If instead at least one assethas no jumps, then the statistic approaches zero in probability. We show how to compute asymptoticallyvalid bootstrap-based critical values that result in a consistent test with asymptotic size equal to or smallerthan the nominal size. Empirically, we study jump linkages between US futures and equity index markets.We find not only strong evidence of jump cross-excitation between the SPDR exchange-traded fund andE-mini futures on the S&P 500 index, but also that integrated jumps in the E-mini futures during theovernight period carry relevant information.