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Robustness of the R/S statistic for fractional stable noises yzx Florin Avram

Summary: Robustness of the R/S statistic for fractional stable noises yzx
Florin Avram
Heriot Watt University
Murad S. Taqqu
Boston University
November 16, 2000
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 di erent 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 in nite variance stable process.
1 Introduction
The R=S statistic provides one of the oldest techniques for detecting long-range dependence and
measuring its intensity. It was discussed by the British physicist H.E. Hurst [10] who studied the
levels of the Nile River. It was later used by Mandelbrot and Wallis [15, 17, 16] to analyze long-range
dependence in geophysical data through a graphical technique which is also described in Mandelbrot
and Taqqu [14] and in the books of Beran [6] and Shiryaev [20]. Its e ectiveness is analyzed in Taqqu,
Teverovsky and Willinger [23] and Taqqu and Teverovsky [22]. A modi ed and non-graphical version
of the R=S statistic, introduced by Lo [11], is discussed in Teverovsky, Taqqu and Willinger [24] and
Willinger, Taqqu and Teverovsky [26]. Bootstrap techniques are presented in Davies and Harte [8]


Source: Avram, Florin - Laboratoire de Mathématiques Appliquées, Université de Pau et des Pays de l'Adour


Collections: Mathematics