Optimal Test for Jump Detection
Tae Suk Lee, Werner Ploberger · ResearchSpace (University of Auckland) · 2009
Suppose one has given discrete observations of a continous-time random process (like e.g. stock market data) and one wants to test for the presence of jumps. Then the power of the tests will depend on the frequency of observations. We show, theat if the data are observed at intervals of lenght 1/n, at best one can detect jumps of height ln(n)/√n. We construct a test which achieves this rate in the case of diffusion-type processes.