We propose a new estimation scheme for estimation of the volatility parameters of a semimartingale with jumps based on a jump detection filter. Our filter uses all of the data to analyze the relative size of increments and to discriminate jumps more precisely. We construct quasi-maximum likelihood estimators and quasi-Bayesian estimators and show limit theorems for them including \(L^p\)-estimates of the error and asymptotic mixed normality based on the framework of the quasi-likelihood analysis. The global jump filters do not need a restrictive condition for the distribution of the small jumps. By numerical simulation, we show that our “global” method obtains better estimates of the volatility parameter than the previous “local” methods.

我们提出了一种新的估计方案，用于基于跳跃检测滤波器来估计带有跳跃的半mart的挥发性参数。我们的过滤器使用所有数据来分析增量的相对大小并更准确地识别跳跃。我们构造了拟极大似然估计器和拟贝叶斯估计器，并基于拟似然分析的框架，给出了它们的极限定理，包括\（L ^ p \） -误差和渐近混合正态性的估计。全局跳转过滤器不需要限制条件来分配小跳转。通过数值模拟，我们表明，与之前的“局部”方法相比，我们的“全局”方法可以获得更好的波动率参数估计。