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

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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.