Study On Tests Of Heavy Tailed Dependent Sequences With Time Varying Scales

Tests of change point and unit root tests are significant research topics in the field of econometrics.Unit root test is an effective method to test the stability of time series in the theoretical and practical research of the economic and financial field,and is also the basis of modeling and cointegration analysis.Considering that financial markets are often affected by external factors that cause sudden changes at one time,it is particularly important to examine the time of sudden changes in order to reduce the risk of miscalculation.A large number of studies have shown that financial data have the characteristics of "spikes and tails" and dependencies.However,current studies mostly focus on the case where the sequence scales are invariable.Therefore,this paper discusses the problems of the unit root tests and tests of mean-change under heavy tail-dependent sequences with time-varying scales.The specific research content is as follows:First,in the study of unit root tests for time-varying heavy tailed dependent sequences,we construct a functional central limit theorem for time-varying scale heavy tailed dependent sequences,and perform non-parametric unbiased estimation of the scale of time series.The limit distribution of the t statistic is obtained.The results of numerical experiments show that the factors affecting the unit root test mainly include the tail index,the scale change amplitude,the change position and the sample size;when the innovation process is compared with dependent and independent,it plays an active role under the original assumption,and the alternative hypothesis is the opposite.We consider the effect of scale fluctuations in the test and give an elimination scale.The consistency of the scale estimation function was tested.The test results after re-examination indicate that the empirical level under the original hypothesis is close to the confidence level,and the correction effect is obvious.Secondly,in the mean-change test of heavy tailed dependent sequences with time varying scales,based on the functional limit theorem proposed in this paper,the limit distribution of statistics under the original hypothesis is obtained,and under the alternative hypothesis,statistics are obtained.The consistency was tested and the results showed that when the mean jump amplitude was ??0,the statistics tends to be infinite as the sample size increases.Then group experiments were conducted on the factors that influence the test.Finally,in the empirical analysis,the data is preprocessed and its heavy-tail characteristics are explored.Next,the mean-change point test is performed.It is found that the statistic value is significantly higher than the critical value,indicating that the sequence contains a mean value change point.