Variation-based tests for volatility misspecification

We provide a simple and easy to use goodness-of-fit test for the misspecification of the volatility function in diffusion models. The test uses power variations constructed as functionals of discretely observed diffusion processes. We introduce an orthogonality condition which stabilizes the limit law in the presence of parameter estimation and avoids the necessity for a bootstrap procedure that reduces performance and leads to complications associated with the structure of the diffusion process. The test has good finite sample performance as we demonstrate in numerical simulations.