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

Methodology