Multiple Change Points Detection Based On Binary Segementation And Its Application In Finance

Change point statistical inference has always been one of important topics of statistics,it is widely used in industrial control,genomics,medical diagnosis,geology,economic,finance,signal processing,fault diagnosis,meteorology and other fields.Change point detection is actually a process of hypothesis testing.This work is interested in how to detect the multiple change points in a sequence.This thesis mainly studies the known observation sequence of change point detection problem,especially the multiple structural change statistical inference in the financial time series.For one dimension normal distribution sequence,we establish a class of multiple change point model containing different types change points.Then we analyze and gain the corresponding likelihood ratio statistics,also the asymptotic properties of estimators is analyzed with the law of large numbers and the law of the iterated logarithm.Further,through the binary segmentation theory,we generalize it to the multiple change point model.Then we use the rule of information criterion and Bayesian model selection to analyze this model and realize a large number of numerical simulations by R software.Finally,the UK house price monthly average index and the highest daily stock price index of Facebook are employed to this model to making empirical analysis.Then we according to the specific background to analysis the practical significance of the change points,including financial crisis,data breach,internal adjustment and so on.We can detect the change point effectively in the process or sequence and make a proper estimation through the analysis of financial time series.The estimation provides very important information to the financial crisis monitoring and forecasting.The estimation is also good for people to evade the risk.