An estimator for the cumulative co-volatility of asynchronously observed semimartingales with jumps
An estimator for the cumulative co-volatility of asynchronously observed semimartingales with jumps
复制标题
具有跳跃的异步观察的半鞅的累积共波动性的估计器
DOI：
10.1111/sjos.12043
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发表时间：
2014
影响因子：
1
通讯作者：
Yuta Koike
中科院分区：
文献类型：
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作者：
澤井周;中原優也;崔埈豪;加藤孝久;巣籠祐介，大澤昇平，松尾豊;上野山勝也，大澤昇平，松尾豊;大澤昇平，松尾豊;大澤昇平，松尾豊;大澤昇平，松尾豊;大澤昇平;大澤昇平;Yuta Koike
本文考虑两个在停时以异步方式采样的半鞅。我们感兴趣的是分别估计它们的累积协波动率和它们的协跳之和。为此目的，我们结合联合收割机的Hayashi-Yoshida方法（处理的双态性）与阈值技术（分离的跳跃），并考虑一类统计量称为截断Hayashi-Yoshida估计。在允许存在无限个活动跳跃的条件下，证明了截断Hayashi-Yoshida估计的相合性和渐近混合正态性。
In this paper, we consider two semimartingales sampled at stopping times in an asynchronous manner. We are interested in estimating their cumulative co‐volatility separately from the sum of their co‐jumps. For this purpose, we combine the Hayashi–Yoshida method (to deal with the asynchronicity) with the threshold technique (to separate the jumps) and consider a class of statistics called the truncated Hayashi–Yoshida estimator. We prove the consistency and the asymptotic mixed normality of the truncated Hayashi–Yoshida estimator under some mild conditions allowing the presence of infinite activity jumps.