Change-point analysis for time series using asymptotic theory for symmetric statistics

使用对称统计渐近理论对时间序列进行变点分析

• 批准号: 20540140
• 负责人: KANAGAWA Shuya
• 金额: $ 2.91万
• 依托单位: Tokyo City University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2008
• 资助国家: 日本
• 起止时间: 2008 至 2012
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20540140/
• 关键词: 変化点解析; 混合性; U-統計量; 確率微分方程式; 数理ファイナンス; 対称統計量; V-統計量; 時系列; 確率解析; ノンパラメトリック統計量; Fuzzy Clustering; AIC; Ginzburg-Landau equation; 非線形回帰分析; SDE; Ginzburg-Landau equations

The aim of the research is to consider an estimation of thechange-point for a s e q u e n c e o f r a n d o m v a r i a b l e s s a t i s f i e s n o t o n l y i n d e p e n d e n c e b u t a l s o some mixing condition from the next reason. Even if these random variables of the sequenceare independent, there possibly exists a regression between them. Especially if they aresequences of linear time series e.g. moving average processes, they satisfy some mixingcondition under the assumptions for their coefficients. We consider not only SDE drivenby a Brownian motion but also by a process with stationary increments from the viewpointsof time series analysis for mathematical finance. For example, when we observe two dataseries of returns for different stocks, it is important to find the regression betweentwo stocks.

研究的目的是考虑对不完全独立且与下一个原因的某些混合条件不满足的随机变量序列的变化点进行估计。即使序列的这些随机变量是独立的，它们之间也可能存在回归。特别是如果它们是线性时间序列的序列，例如移动平均过程，它们在系数假设下满足某些混合条件。从数学金融时间序列分析的角度来看，我们不仅考虑由布朗运动驱动的 SDE，而且还考虑由平稳增量过程驱动的 SDE。例如，当我们观察不同股票的两个收益数据系列时，找到两只股票之间的回归非常重要。

项目成果

Approximated solution of Ginzburg-Landau equation induced from nearly bichromatic wave

近双色波导出的Ginzburg-Landau方程的近似解

• 发表时间: 2010
• 作者: S. Kanagawa;K.Tchizawa and T.Nitta
• 通讯作者: K.Tchizawa and T.Nitta

Fuzzy Node Fuzzy Graph Analysis Applying T-norm

应用 T 范数的模糊节点模糊图分析

• 发表时间: 2012
• 期刊: Biomedical Soft Computing and Human Sciences
• 作者: H. Uesu;S. Kanagawa
• 通讯作者: S. Kanagawa

Statistical Scheme via AIC for Evaluating the Optimal Cut Off Level in Fuzzy Clustering

通过 AIC 评估模糊聚类中最佳截止水平的统计方案

• 期刊: Proceedings of the 2011 IEEE International Conference on Fuzzy Systems
• 作者: S.Kanagawa;K.Shinkai;H.Chung;K.Nagashima
• 通讯作者: K.Nagashima

Change-point problems for coefficients of stochastic differential equations driven by stationary increments sequence

平稳增量序列驱动的随机微分方程系数的变点问题

• 发表时间: 2008
• 作者: S.Kanagawa;K.Yoshihara
• 通讯作者: K.Yoshihara

Limit Theorems for Hilbert Space Valued Random Variables and their Applications to Investigation of Asymptotic Behaviors of Symmetric Statistics

希尔伯特空间值随机变量的极限定理及其在对称统计渐近行为研究中的应用

• 发表时间: 2012
• 作者: S.Kanagawa