Nonsynchronous covariation process and limit theorems
Nonsynchronous covariation process and limit theorems
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DOI：
10.1016/j.spa.2010.12.005
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发表时间：
2011-10-01
影响因子：
1.4
通讯作者：
Yoshida, Nakahiro
中科院分区：
文献类型：
--
作者：
Hayashi, Takaki;Yoshida, Nakahiro
给出了连续半鞅非同步协变过程的渐近分布理论。两个连续半鞅在停时以非同步方式采样。这些采样时间可能取决于随机过程的历史和随机过程本身。当采样区间的最大值趋于零时，非同步协变过程收敛于半鞅的二次协变。我们处理的情况下，归一化逼近误差的极限变差过程是随机的，并证明了收敛到混合正规，或收敛到条件高斯鞅。提出了一类基于核函数的渐近变差过程的相合估计，这将有助于金融高频数据分析的统计应用。作为一个说明性的例子，讨论了具有随机变点的泊松抽样方案。(C)2010爱思唯尔有限公司版权所有。
An asymptotic distribution theory of the nonsynchronous covariation process for continuous semimartingales is presented. Two continuous semimartingales are sampled at stopping times in a nonsynchronous manner. Those sampling times possibly depend on the history of the stochastic processes and themselves. The nonsynchronous coyariation process converges to the usual quadratic covariation of the semimartingales as the maximum size of the sampling intervals tends to zero. We deal with the case where the limiting variation process of the normalized approximation error is random and prove the convergence to mixed normality, or convergence to a conditional Gaussian martingale. A class of consistent estimators for the asymptotic variation process based on kernels is proposed, which will be useful for statistical applications to high-frequency data analysis in finance. As an illustrative example, a Poisson sampling scheme with random change point is discussed. (C) 2010 Elsevier B.V. All rights reserved.