Properties of a specification test for the parametric form of the variance function in diffusion processes dXt = b (t,Xt) dt + sigma (t,Xt) dWt are discussed. The test is based on the estimation of certain integrals of the volatility function. If the volatility function does not depend on the...

This work develops change-point methods for statistics of high-frequency data. The main interest is the volatility of an Itô semi-martingale, which is discretely observed over a fixed time horizon. We construct a minimax-optimal test to discriminate different smoothness classes of the...