Jump-robust testing of volatility functions in continuous time models

In this article, we develop new tests for the parametric volatility function of jump-diffusion processes. Our tests are of the Kolmogorov-Smirnov and Cramer-von Mises types, and are based on marked empirical processes coupled with a threshold bipower approach. The tests impose no restrictions on the functional form of the drift function and are robust to jumps. Monte Carlo simulations show that the tests have satisfactory size and good power under processes with or without jumps. Application to a real dataset shows that our jump-robust volatility tests give more reasonable results than the existing non-robust volatility tests.