Self-normalized Wilcoxon Test For Change Points In Long Memory Time Series

In the study of change points in long memory time series,the constructed test statistic usually has unknown long run variance and it is difficult to give a consistent estimate of the long run variance.By recursively estimating the parameters,the self-normalized approach constructs the variance only related to the sample to replace the long run variance,which not only avoids estimating the long run variance,but also achieves a better test effect.In addition,most test methods based on raw data to construct statistics are significantly affected by outliers,while statistics based on data rank are more robust.In this paper,testing for change points in long memory time series is studied based on self-normalized Wilcoxon test.Under the single change point model,the change point in mean and trend are studied respectively.In the process of studying the changes in mean,it is found that the empirical power of the self-normalized Wilcoxon test is low when the change point is close to the two ends,which is also a problem of many single change point test methods.By modifying the self-normalized Wilcoxon method,the empirical power when the change point is close to the two ends is improved.The main idea is to reduce the sample size difference before and after the change point by intercepting the sequence,so as to achieve the purpose of improving the empirical power.The simulation results show that the modified method can improve the empirical power when the change point is close to both ends.In the case analysis,through the analysis of a set of the annual volume of discharge from the Nile data,it is further verified that the modified method is more effective than the original method when the change point is close to the two ends.When testing the change point in trend,the original sequence is first differenced,and self-normalized Wilcoxon test statistics are constructed based on the data after first-order difference.Under the null hypothesis the limiting distribution of the test statistics is deduced,and under the alternative hypothesis proved the consistency of the test statistics.In addition,the influence of intercept and variance change points on the test method is further studied.The simulation results show that this method can effectively test change point in trend,and is robust to intercept and variance change points when the sample size is large.Finally the analysis of a set of the S?P 500 index data verifies the validity of the method.The test and estimation of the multiple change points in mean is studied and a new NOT test method based on the self-normalized Wilcoxon statistic is proposed,which is denoted as the NOT-SNW method in this article.The core of the method is to use the self-normalized Wilcoxon test statistic to find the segmentation point,randomly extract several subsamples from the sequence and calculate the value of the test statistic for each subsample.Then find out the subsample that exceeds the critical value and has the smallest sample size,and obtain the point that makes the statistics reach the maximum in this subsample.The point obtained from the above process is segmentation point and also the estimation of location of change point.The effectiveness of the method is studied by simulation under two multiple change-point models,and compared with WBS,PELT and other methods.The simulation results show that the performance of the NOT-SNW method is equivalent to that of other methods under normal conditions,but the estimation stability is slightly poor.In the case of long memory,with the enhancement of long memory,other methods are greatly influenced by it,while the NOT-SNW method can still effectively test change points and is robust to outliers.Finally,a set of OPEC oil price data is analyzed,and the analytical results are basically consistent with the actual situation.