Statistical Inference Of Mean Change Point Under Heavy-Tailed Sequence And Its Application

Modeling and predicting analysis of financial markets volatility is a hot topic in the field of econometric.Many financial data have been found to be non-stationary with a "spike thick tail" feature,and their distribution presents a greater tail probability than the normal distribution,resulting in a large amount of data information remaining in the tail.The structural change point is an important reason for the instability of time series data.Therefore,it is very necessary to perform effective structural change point detection before constructing the econometric models.The mean value is an important feature of financial data,so this paper focuses on the statistical inference of mean change point under the heavy-tailed dependent series.The specific contents are as follows.Aiming at the defects that the classical cumulative-sum test statistic is easily affected by the location of change point,the modified form is constructed by reversing the statistic,so as to realize the mean change point test under heavy-tailed dependent sequence.The theorems prove the limit distribution of the modified cumulative-sum test statistic under the null hypothesis and the alternative hypothesis.In view of the dependence and heavy tail of the sequence,the critical value of the asymptotic distribution of statistic are determined by using Block Bootstrap sampling method.The numerical simulation results indicate that the modified test statistic overcomes the defect that the original statistic depends on the position of the change point,and the empirical power also increases significantly.To improve the test efficiency,a new Ratio test statistic is proposed.Based on the generalized central limit theorem,the asymptotic distribution of test statistic under the null hypothesis is obtained,and the consistency of the test is proved under the alternative hypothesis.The numerical simulation results show that the Ratio test can not only control the experience size well,but also has a certain improvement in the empirical power compared with the previous modified cumulative-sum test methods.Finally,in order to further verify the feasibility and effectiveness of the mean change point test methods proposed in this article,two sets of financial stock data are selected for empirical analysis.The results make clear that the Ratio statistic based on Block Bootstrap sampling is an effective detection tool for the mean change point problem.