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Essay 1 (Job Market Paper)

"An Improved Pre-averaging Estimator of Integrated Volatility" 

(Previous version: Pre-averaging Estimator of Realized Variance)

(with Werner Ploberger)

         Although ultra high frequency financial data become available with technological progress, there is still a problem to measure intra-daily volatility of return because of so called market microstructure noise. Previous solutions have used relatively coarse sampling frequency such as 20 minutes or have utilized more data under specific assumptions of micro-structure noise. However, losing parts of data or assuming an exogenous white noise may cause a loss of accuracy.
        We investigate pre-averaging estimators first defined by Podolskij and Vetter (2009). We relax the assumptions on microstructure noise to include realistic features of noise like missing data, flat trading etc. We develop an explicit asymptotic theory of our estimator using martingale convergence theorems. Especially we deal with the boundary problem of pre-averaging and present a new solution to this problem. Based on the theory, we show that general linear combination of estimators can be made unbiased and devise a rate-optimal estimator of integrated variance. We also derive a bootstrap statistic to assess the variance of the estimator which allows us to optimize our smoothing parameter from the data. Since our methodology and assumptions on noise are general, our estimator can be applied in multivariate data without correction for asynchronous trades. Monte Carlo experiments show our theoretical results are valid in realistic cases.

Essay 2

"Rate-optimal Tests for Jumps in Diffusion Processes" 

(with Werner Ploberger)

      Continuous diffusion models have provided a simple, flexible, and powerful tool to analyze economic and financial data since the time before high frequency data become available. However, the continuous diffusion models do not capture jumps in high frequency data. As a result the jump diffusion model was introduced. Therefore researcher must know whether the data contain jumps or not. Though several tests (Barndorff-Nielsen and Shephard (2002), Ait-Sahalia and Jacod (2009)) were introduced, their power properties were not explicitly considered.
       Our aim is to propose a rate-optimal test for the null hypothesis of continuous diffusion models against an alternative hypothesis of jump diffusion models. From the likelihood ratio, we derive the local power bound, the minimum size of jump which can be detected with nontrivial power. Then we construct a rate-optimal test in the case of diffusion-type processes. It can detect a jump the size of which is greater or equivalent to the local power bound. With simulation experiments, we show that our tests have excellent size and power properties for realistic sample sizes. Applying our tests to many high frequency data (e.g. foreign exchange rates, stock indices, and Dow30 stock prices), we find more jumps in the data than are found by other tests.