Avram, Florin; Taqqu, Murad S. Robustness of the \(R/S\) statistic for fractional stable noises. (English) Zbl 0968.62037 Stat. Inference Stoch. Process. 3, No. 1-2, 69-83 (2000). Summary: The \(R/S\) statistic is used to detect long-range dependence in a time series and to estimate its intensity. One of its virtues is robustness against different distributions. We show here that the \(R/S\) statistic continues to be robust if the time series is a moving average with long-range dependence with innovations that are in the domain of attraction of an infinite variance stable process. MSC: 62F35 Robustness and adaptive procedures (parametric inference) 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 60G18 Self-similar stochastic processes 62F12 Asymptotic properties of parametric estimators 60E07 Infinitely divisible distributions; stable distributions 60F17 Functional limit theorems; invariance principles Keywords:self-similar processes; functional limit theorems; stable distributions; weak convergence; Skorokhod topology PDFBibTeX XMLCite \textit{F. Avram} and \textit{M. S. Taqqu}, Stat. Inference Stoch. Process. 3, No. 1--2, 69--83 (2000; Zbl 0968.62037) Full Text: DOI