Statistical Inference Of Mean Change Point Of Dependent Sequence Under Time-Varying Volatility

For the past four decades,the problem of change point has been one of the hot issues in the field of statistical research.Ignoring the influence of structural changes will lead to inaccurate predictions and incorrect statistical analysis,so it is especially necessary to effectively test structural changes before building a model.The study found that:on the one hand,many financial time series data do not simply obey an independent distribution,and there are often certain dependencies between sequences;on the other hand,the mean value,as an important numerical feature of financial data,can well describe the level change of the time series.Therefore,this article mainly focuses on the test of the change point of the mean change point of the dependent sequence.The specific research content is as follows:Compared with the classical cumulative sum statistics,the ratio test statistic is used to study the test of the change point of the mean of the dependent series.In the mean change point model,it is theoretically proved that the limit distribution of the ratio statistic under the null hypothesis is a functional of the standard Brownian motion,and the consistency of the statistic is proved under the alternative hypothesis.Numerical simulation results show that the empirical size fluctuates around the testing significant level;the empirical potential power increases with the increase of sample size and the jump size of the mean change;the empirical potential power of the mean change point in the middle of the sample is significantly higher than the value of the empirical potential power at the previous and later periods of the mean change point.In view of the fact that many financial data have non-stationary volatility,the problem of testing the mean change points of dependent series in the case of heteroscedasticity is discussed.Based on the generalized central limit theorem,the limit distributions of the ratio statistic in the case of heteroscedasticity under the null hypothesis and the alternative hypothesis are deduced respectively.The asymptotic distribution under the null hypothesis is no longer a functional of the standard Brownian motion,but depends on the specific expression of the variance function.The study found that the empirical size under heteroscedasticity will be severely distorted,and the testing significant level is no longer approached.In response to this defect,this article proposes a modified ratio test statistic to achieve an effective test of the mean change point under heteroscedasticity.Numerical simulation results show that the modified ratio test statistics can improve the distortion of empirical size and the loss of empirical potential power.Finally,two sets of time series data of Shanghai Pudong Development Bank stock price and the lowest water level of the Nile River are selected for empirical analysis.The results show that the modified ratio test method proposed in this article is effective and feasible.The study of the mean change point under time-varying fluctuations based on ratio statistics has important theoretical significance and application value in the field of econometrics.