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In this paper, we propose a new threshold-kernel jump-detection method forjump-diffusion processes, which iteratively applies thresholding and kernelmethods in an approximately optimal way to achieve improved finite-sampleperformance. We use the expected number of jump misclassifications as theobjective function to optimally select the threshold parameter of the jumpdetection scheme. We prove that the objective function is quasi-convex andobtain a new second-order infill approximation of the optimal threshold inclosed form. The approximate optimal threshold depends not only on the spotvolatility, but also the jump intensity and the value of the jump density atthe origin. Estimation methods for these quantities are then developed, wherethe spot volatility is estimated by a kernel estimator with thresholding andthe value of the jump density at the origin is estimated by a density kernelestimator applied to those increments deemed to contain jumps by the chosenthresholding criterion. Due to the interdependency between the model parametersand the approximate optimal estimators built to estimate them, a type ofiterative fixed-point algorithm is developed to implement them. Simulationstudies for a prototypical stochastic volatility model show that it is not onlyfeasible to implement the higher-order local optimal threshold scheme but alsothat this is superior to those based only on the first order approximationand/or on average values of the parameters over the estimation time period.

Optimal Iterative Threshold-Kernel Estimation of Jump Diffusion Processes