Estimating diffusion with compound Poisson jumps based on self-normalized residuals

We consider parametric estimation of the continuous part a class ergodic diffusions with jumps based on high-frequency samples. Various papers previously proposed threshold methods, which enable us to distinguish whether observed increments have or not at each small-time interval, hence estimate unknown parameters separately. However, data-adapted and quantitative choice parameter is known be subtle sensitive problem. In this paper, we present simple alternative Jarque–Bera normality test for Euler residuals. Different from method, method does require any fine tuning, practical value. It shown that under suitable conditions estimator asymptotically equivalent an constructed by unobserved fluctuation solution process, efficient. Some numerical experiments are conducted observe finite-sample performance method.