Testing and Detecting Jumps Based on a Discretely Observed Process

We propose a new nonparametric test for detecting the presence of jumps in asset prices using discretely observed data. Compared with the test in Ait-Sahalia and Jacod (2009), our new test enjoys the same asymptotic properties but has smaller variance. These results are justified both theoretically and numerically. We also propose a new procedure to locate the jumps. The jump identification problem reduces to a multiple comparison problem. We employ the false discovery rate approach to control the probability of type I error. Numerical studies further demonstrate the power of our new method.