Statistical Inference for Duration Model using High-Frequency Financial Time Series

在高频金融时间序列的分析中，与京都大学经济研究所的西山良彦教授共同进行了“多变量综合波动率的非参数估计”的研究，从理论和模拟的角度考虑了Malliavin-Mancino估计和Hayashi-Yoshida估计，探讨了非同步观测的多维扩散过程的波动率的估计方法。我们的结论是，Hayashi-Yoshida估计是上级。在与Song Mingzi的联合研究“Multivariate Ito Processes的高频观测的非参数估计”中，我们利用半鞅局部时的估计，给出了Ito过程的多元波动率的非参数估计;在“Nonlinear renewal theories for random walks with intermediate order扰动，“（与张存辉），我们证明了一个具有扰动项的随机游动的非线性更新定理，这在统计序列分析理论中变得很重要。我们将其应用于非参数序贯概率比检验，并在2007年日本统计学会会议特邀会议上发表的论文中提出了以序贯检验方式进行单位根检验的新方法。

For the analysis using high-frequency financial time series, a joint research "Nonparametric Estimation of Multivariate Integrated Volatilities" with Prof. Yosihiko Nishiyama of Institute of Economic Research, Kyoto University is about the estimate manner of volatility of multi-dimensional diffusion process observed nonsynchronously, in which we consider the Malliavin-Mancino estimator and the Hayashi-Yoshida estimator from views of theory and simulation. We conclude that the Hayashi-Yoshida estimator is superior. We also estimated the covariance using government bond futures tick data as empirical study.In the joint research "Nonparametric Estimation for the High Frequency Observations of Multivariate Ito Processes" with Song Mingzi, we provide a nonparametric estimator of multivariate volatility of Ito processes which exploits the estimator of the local time of semimartingale.In "Nonlinear renewal theorems for random walks with perturbations of intermediate order," (with Cun-Hui Zhang), we prove a nonlinear renewal theorem for a random walk having perturbation terms, which is becoming important in a theory of statistical sequential analysis. We apply it to the nonparametric sequential probability ratio test.We also suggest new method of performing a unit root test by manner of a sequential test in the paper reported in the invited session of the meeting of Japanese Statistical Association in 2007.