| The central theme of my dissertation is the econometric inference for jumps in high-frequency financial time series. I ask two questions. Firstly, it is well known that high-frequency data are contaminated by the microstructure noise. How to make robust statistical inference on jump characteristics in a noisy setting? Secondly, based on nonparametric methods, the literature has documented that jumps are prevalent in the data. However, these findings are often based on purely statistical measures of the jump signal and thus lack a clear economic interpretation. How to measure and make inference on the economic significance of jumps?;Chapters 1 and 2 show how to conduct robust inference on power variations of jumps (PVJ). In chapter 1 (joint with Yacine Ait-Sahalia and Jean Jacod), we take the PVJ as a measure of the jump signal and use it to construct tests for jumps. We use the pre-averaging method to robustify our test against microstructure noise. Simulation evidence supports the theoretical claim on robustness. However, we find that standard asymptotic theory does not provide a good approximation for the finite-sample behavior of the pre-averaging estimator unless jumps are either absent or very large, making the inference for small jumps in a noisy environment challenging. I attack this problem in chapter 2 by developing a new local asymptotic theory in a setting in which jumps are possibly small, modeled as local-to-zero with an unknown vanishing rate. I then construct a robust confidence interval for the PVJ which has correct asymptotic coverage no matter what the jump size is. I also apply this local asymptotic theory to study the power properties of the tests proposed in the first chapter.;In chapter 3, I measure the economic significance of jumps by the hedging error they induce. I introduce the notion of jump error profile, defined as the collection of jump-induced delta-hedging errors of a family of European options. I construct formal tests for the positivity of the jump error profile. An empirical application on U.S. stocks shows that jumps cause statistically significant and economically sizable hedging errors for short-dated vanilla options. |
