Nonparametric Inference of Jump Autocorrelation

Understanding the jump dynamics of market prices is important for asset pricing and risk management. Despite their analytical tractability, parametric models may impose unrealistic restrictions on the temporal dependence structure of jumps. Using nonparametric technique, we develop an omnibus test for the temporal dependence of jump occurrences in the DGP. It delivers consistent test result under a unified framework that combines and long-span and in-fill asymptotics, and is robust to the jump activity level and the choice of sampling scheme. We also study the use of sample autocorrelogram for visualizing and conducting pointwise inference of the autocorrelation of jump occurrences. We establish asymptotic normality and local power of the inference procedures for a rich set of local alternatives (e.g., self-exciting and/or self- inhibitory jumps). Simulation study confirms the robustness property of the omnibus test and reveals its competitive size and power performance relative to existing tests. In an empirical study on high-frequency stock returns, our procedure uncovers a wide array of autocorrelation profiles of jump occurrences for different stocks in different time periods.