Before revision:  We also demonstrate that the level of the endogeneity of markets, quantified by the branching ratio of the Hawkes process, is overestimated if the time-variation is not considered .
After revision:  We also demonstrate that the level of the endogeneity of markets, estimated by our model is 0.41, suggesting the relative importance of exogenous factors in the market dynamics. We also demonstrate that it is critically important to appropriately model the time-dependent background rate for the branching ratio estimation .