Nonparametric Transition-Based Tests for Jump-Diffusions

We develop a specification test for discretely-sampled jump-diffusions, based on a comparison of a nonparametric estimate of the transition density or distribution function to their corresponding parametric counterparts. As a special case, our method applies to pure diffusions. We propose three different discrepancy measures between the null and alternative transition density and distribution functions. We establish the asymptotic null distributions of proposed test statistics and compute their power functions. The finite sample properties are investigated via simulation studies and are compared with those of alternative tests