In this paper, we use intraday futures market data on gold and oil to compute returns, realized volatility, volatility jumps, realized skewness and realized kurtosis. Using these daily metrics associated with two markets over the period of December 2, 1997 to May 26, 2017, we conduct linear, nonparametric, and time-varying (rolling) tests of causality, with the latter two approaches motivated due to the existence of nonlinearity and structural breaks. While, there is hardly any evidence of spillovers between the returns of these two markets, strong evidence of bidirectional causality is detected for realized volatility, which seems to be resulting from volatility jumps. Evidence of spillovers are also detected for the crash risk variables, i.e., realized skewness, and for realized kurtosis as well, with the effect on the latter being relatively stronger. Based on a moments-based test of causality, evidence of co-volatility is deduced, whereby we find that extreme positive and negative returns of gold and oil tend to drive the volatilities in these markets. In our robustness check, we identify a causal chain in the realized volatility from oil to gold via the financial stress. Our results have important implications for not only investors, but also policymakers.