Power Variations and Testing for Co-Jumps: The Small Noise Approach
Power Variations and Testing for Co-Jumps: The Small Noise Approach
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功率变化和共跳测试：小噪声方法
DOI：
10.1111/sjos.12309
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发表时间：
2017
影响因子：
1
通讯作者：
Kurisu Daisuke
中科院分区：
文献类型：
--
作者：
Kunitomo Naoto;Kurisu Daisuke;Awaya Naoki;栗栖大輔;栗栖大輔;Kurisu Daisuke
In this paper, we study the effects of noise on bipower variation, realized volatility (RV) and testing for co‐jumps in high‐frequency data under thesmallnoise framework. We first establish asymptotic properties of bipower variation in this framework. In the presence of the small noise, RV is asymptotically biased, and the additional asymptotic conditional variance term appears in its limit distribution. We also propose consistent estimators for the asymptotic variances of RV. Second, we derive the asymptotic distribution of the test statistic proposed in (Ann. Stat. 37, 1792‐1838) under the presence of small noise for testing the presence of co‐jumps in a two‐dimensional Itô semimartingale. In contrast to the setting in (Ann. Stat. 37, 1792‐1838), we show that the additional asymptotic variance terms appear and propose consistent estimators for the asymptotic variances in order to make the test feasible. Simulation experiments show that our asymptotic results give reasonable approximations in the finite sample cases.
