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

本研究的目的是考虑S与S、S与S、S与L、S等人在某种混合条件下的转折点估计。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。特别是当它们是线性时间序列，如移动平均过程时，它们在系数的假设下满足一定的混合条件。从数学金融的时间序列分析的观点出发，我们不仅考虑布朗运动驱动的随机过程，而且考虑平稳增量过程驱动的随机过程。例如，当我们观察不同股票的两个收益数据序列时，找到两个股票之间的回归是很重要的。

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.