Asymptotics for functionals of self-normalized residuals of discretely observed stochastic processes
Asymptotics for functionals of self-normalized residuals of discretely observed stochastic processes
复制标题
离散观测随机过程的自归一化残差泛函的渐近
DOI：
10.1016/j.spa.2013.03.013
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发表时间：
2013
影响因子：
1.4
通讯作者：
H. Masuda
中科院分区：
文献类型：
--
作者：
X. Huang;塩沢裕一;H. Masuda and N. Yoshida;渡部善隆,藤原宏志,中尾充宏;Kaoru Fujioka;H. Masuda;Kaoru Fujioka;Y. Iso and H. Fujiwara;Yuichi Shiozawa;H. Masuda
本文的目的是得到一类高频观测的扩散型过程的自归一化残差泛函的随机展开式，其中总观测周期可能趋于无穷，也可能不趋于无穷大。这一结果使我们能够针对“跳跃分量的存在”和“扩散系数误指定”，为拟合优度检验构造一些明确的统计量；然后，对零假设的接受可以作为使用正确指定的扩散类型模型的附带证据。特别是，我们的渐近结果阐明了如何消除由于插入扩散系数估计而引起的偏差。
The purpose of this paper is to derive the stochastic expansion of self-normalized-residual functionals stemming from a class of diffusion type processes observed at high frequency, where total observing period may or may not tend to infinity. The result enables us to construct some explicit statistics for goodness of fit tests, consistent against “presence of a jump component” and “diffusion-coefficient misspecification”; then, the acceptance of the null hypothesis may serve as a collateral evidence for using the correctly specified diffusion type model. Especially, our asymptotic result clarifies how to remove the bias caused by plugging in a diffusion-coefficient estimator.