The Statistical Inferences On Change Points In Time Series

Time series data are common in real life,we often use models to describe them.But it's not reasonable to describe the longer time series with a simple model.A reasonable approach is to divide the whole time series into several segments,each of which follows a simple time series model.Time series models of different fragments do not have to be the same model.We called the time between two adjacent segments a change point.In this paper,we propose a hypothesis testing method to detect the change points in the whole time series.First,the stationary test statistic is defined,and then the stationarity test scanning method is made.The scanning method transforms the multiple-change-point estimation problem into a single change point estimation problem,and determines the number of the final change points and the location of the change point.Furthermore,the distribution of change point estimation is obtained by using the bootstrapping method.Simulation experiments show that our hypothesis testing method gives very accurate estimation of change point and the distribution of change point estimation.Finally,we apply this method to a set of real time series data.