Statistical Inference for Jump Coefficients in High-Frequency Data

This thesis investigates the statistical estimation of jump regression coefficients between two Itô semimartingales using high-frequency data. Building upon the framework established by Li, Todorov, and Tauchen, we extend their analysis by relaxing the assumption of an exact linear relationship between the processes, thereby explicitly accounting for idiosyncratic jump noise. We propose a non-parametric estimator and rigorously derive its asymptotic properties, establishing both consistency and asymptotic normality. The theoretical analysis is conducted under two distinct regimes: a fixed time horizon with the observation mesh size tending to zero, and an extension to an infinite time horizon. The work is organized as follows: We first revisit the fundamental theory of stochastic processes and semimartingales, leading into the specific properties of Itô semimartingales. We then introduce the model setting and the necessary technical assumptions. Subsequently, we present the proposed estimators, establish their consistency, and derive their asymptotic distributions. Following the finite horizon analysis, we extend the framework to an infinite time horizon, a setting that necessitates a distinct threshold specification. Finally, we present Monte Carlo simulation results to illustrate the finite-sample performance of the estimators under simplified parametric settings and discuss practical considerations for implementation.