The optimal rate of convergence of estimators of the integrated volatility,for a discontinuous It\^{o} semimartingale sampled at regularly spaced timesand over a fixed time interval, has been a long-standing problem, at least whenthe jumps are not summable. In this paper, we study this optimal rate, in theminimax sense and for appropriate "bounded" nonparametric classes ofsemimartingales. We show that, if the $r$th powers of the jumps are summablefor some $r\in[0,2)$, the minimax rate is equal to $\min(\sqrt{n},(n\logn)^{(2-r)/2})$, where $n$ is the number of observations.
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机译：对于以固定间隔和固定时间间隔采样的不连续It \ ^ {o}半mart鱼，综合波动率估计量的最优收敛速度一直是一个长期存在的问题，至少在跳数不可求和的情况下。在本文中，我们以最小极大值和适当的“有限”半参量非受限类别研究了最佳比率。我们表明，如果某次$ r \ in [0,2）$的跃迁的$ r $ th次幂是可累加的，则最小最大速率等于$ \ min（\ sqrt {n}，（n \ logn）^ {（2-r）/ 2}）$，其中$ n $是观察数。
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