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

对于使用高频金融时间序列的分析，京都大学经济研究所西山义彦教授与其合作的《多变量综合波动率的非参数估计》是关于非同步观测到的多维扩散过程波动率的估计方式，我们从理论和模拟的角度考虑了Malliavin-Mancino估计和Hayashi-Yoshida估计。我们的结论是林-吉田估计量是更好的。在与宋明子合作的《多元Ito过程高频观测值的非参数估计》中，我们利用半马尔科夫过程局部时刻的估计，给出了Ito过程多元波动率的一个非参数估计。在与张存辉合著的《带有中阶扰动的随机游动的非线性更新定理》中，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，这在序贯统计分析理论中具有重要意义。我们将其应用到非参数序贯概率比检验中，并在2007年日本统计学会特邀会议上发表的论文中提出了用序贯检验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.