High-Frequency Cross-Market Trading: Model-Free Measurement and Testable Implications

This paper develops a model-free measurement and inference framework for high-frequency cross-market trading activity and provides empirical evidence of its importance in financial markets. We represent trading activity in two markets as temporal point processes and count the number of time bins in which both processes register activity at a given lag. Under the null of cross-process independence, without global stationarity, a Chen–Stein approximation yields Poisson convergence in total variation for this simple bin-based measure of cross-activity under mild regularity conditions. A local-stationarity framework for marginal intensities, allowing finitely many jumps, then yields a feasible blockwise estimator of the null Poisson mean. The resulting feasible asymptotic theory leads to three easy-to-implement statistical tests for independence at a given lag. It further yields consistent score-driven identification of dependence lags caused by lagged common components in market activity, characteristic of linked order executions across markets. This novel identification framework exploits that common components induce a singular line mass and Poisson score divergence at latency-determined dependence lags. Monte Carlo experiments with nonstationary superpositions of Hawkes processes confirm satisfactory test size, power, and lag-identification performance in finite samples. Empirical validation using transaction data for U.S. Treasury and equity cash-futures markets from 2010 to 2024 reveals sharply localized cross-activity dependencies at lags matching microwave latency, while not rejecting independence at more distant lags. High-frequency cross-market trading generally intensifies during market stress episodes and exhibits pronounced intraday surges after FOMC announcements, confirming its role in information propagation and efficient price discovery across linked markets.