Persistence Change Point Detection Based On Ratio Tests And Its Application

As one of the significant branches of time series analysis,change point study has important theoretical significance and presents a broad application prospect.Relevant researches show that whether the series is stationary or not impacts a lot on the application effect of a model.Due to the fact that traditional test methods mostly base on homoscedasticity assumption and therefore have some limitation,the deeper studies of persistence change points are particularly important.Basing on the background above,this paper have done an advanced research to study the performance of traditional test statistics for persistence change under the heteroscedasticity assumption.Firstly,under the consideration of break point types and changes of statistical limiting distribution,we assume that the variance of error term is dynamic variation and give the new different limiting distribution.Secondly,we prove the estimation effects of corresponding statistics and give two theorems to summarize the influence brought by appearance position of heteroscedasticity,change magnitude and persistence change position on estimation effects.Results show that heteroscedasticity will extremely increase the size of test and decrease its power.Meanwhile,it will make statistics estimate a wrong position.Thirdly,we generally analysis statistics basing on regression residuals and point out that heteroscedasticity leads OLS estimators are no longer the best linear unbiased estimate.In order to eliminate the bad influence of regression residuals,we propose a feasible generalized least squares method,which based on weighed OLS.The corresponding numerical simulation shows that our methods work well,especially for the test statistic whose null hypothesis is stationary and can release the size significantly without a power loss.At last,apply the modified method to the data of Trade Weighted U.S.Dollar Index(TWEXB)and U.S./Euro Foreign Exchange Rate(EXUSEU)and the results show that our methods improve a lot compared with the traditonal ones.The research results in this paper are useful supplements and improvements to the test theory of persistence change point,which have certain theoretical significance,and have certain application value in the field TWEXB,EXUSEU and so on.