Testing for diffusion in a discretely observed semimartingale

Using pth power variation, we propose a nonparametric method to test whether a continuous diffusion is present in a semimartingale. Under the discrete observation of high frequency data, the test statistic converges to a known constant if a diffusion is present, otherwise it tends to another number. The test procedure is valid for all Itô semimartingales and does not depend on the law of a process or the coefficients of a semimartingale. We also implement the test on simulation and real asset return data.