On discriminating between long-range dependence and changes in mean

摘要: We develop a testing procedure for distinguishing between long-range dependent time series and weakly with change-points in the mean. In simplest case, under null hypothesis is one change mean at an unknown point, alternative it dependent. compute CUSUM statistic T n , which allows us to construct estimator k of change-point. then n,1 based on observations up n,2 2 after k. The M = max[T n.1 ] converges well-known distribution null, but diverges infinity if exhibit dependence. theory illustrated by examples application returns Dow Jones index.