Estimating Diffusion With Compound Poisson Jumps Based On Self-normalized Residuals
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This paper considers parametric estimation problem of the continuous part of a jump dif- fusion model. The threshold based method was previously proposed in various papers, which enables us to distinguish whether observed increments have jumps or not, and to estimate unknown parameters. However, a data-adapted and quantitative choice of the threshold parameter is a subtle and sensitive problem, and still remains as a tough problem. In this paper, we propose a new and simple alternative based on the Jarque-Bera normality test, which makes us to attain the above two things without any sensitive fine tuning. We show that under suitable conditions the proposed estimator has a consistency property. Some numerical experiments are conducted.
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