Research On Structural Change Of Heavy-tailed Sequence

The variable point problem is widely used in astronomy,communication,medicine,meteorology,industrial automatic control and many other fields of humanities and science.The change-point research also enriches the theory of s-tatistical diagnosis and statistical modeling.The study has important theoretical value.The research results of the change-point problem can provide reference for people's decision-making and preventive measures for possible risks.Therefore,the study of change-point has always been the focus of attention in the academic community.Especially in the economic and financial,many financial assets such as stocks and bonds have the characteristics of“spike”and“heavy tail”,which cannot be described by normal distribution.Therefore,the research on change-point of heavy-tailed sequence has high research value.Since the heavy tail index ? is difficult to estimate in practical application,the parametric method is no longer applicable to study the change-point of heavy-tailed sequence.Therefore,the non-parametric method is used in this paper to discuss the existence of mean change of heavy-tailed sequence.The contents of the thesis are as follows:(1)We consider Ratio test for mean change in heavy-tailed sequence.The Ratio test method is used to construct a test statistic based on the CUSUM function and the ratio of the cumulative sum of squares of the residuals.When the null hypothesis condition is established,the limit distribution of the residual cumulative square sum ratio test statistic is a Lévy process function.Finally,Monte Carlo numerical simulations verify that this method is effective.(2)We studied the empirical likelihood ratio test for the mean change of the heavy-tailed sequence.Firstly,based on the heavy-tailed observations,the empirical likelihood functions are obtained under the null hypothesis and the al-ternative hypothesis.Secondly,the likelihood ratio test statistics are constructed based on the empirical likelihood function.The asymptotic distribution of the likelihood ratio statistic is given when the null hypothesis is established.Finally,Monte Carlo numerical simulations verify that the method has a good effect on the detection of the mean change of heavy-tailed sequence.