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Robustness of the \(R/S\) statistic for fractional stable noises. (English) Zbl 0968.62037

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
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