B. Mandelbrot, "Robust R/S analysis of long run serial correlation," in Proc. 42nd Session ISI, pp. 69--99, 1979.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....process, it is sufficient to estimate fi which is given by the slope of the diagram log 10 (var(X (m) oe 2 ) against log 10 (m) The estimated slope fi gives an estimate of H : H = 1 Gamma fi=2. Note that other methods are available to estimate H: R S statistics proposed by Mandelbrot [15] and periodograms [6] In our context, we estimate the local Hurst parameter H l . In Figures 2, 3 and 4, the variance time plot is given for a Markov chain having the structure described in 2.3. In addition, a line indicates the slope of Gamma1 (Hurst=0:5) According to the Figures, we see that ....

B. Mandelbrot, "Robust R/S analysis of long run serial correlation," in Proc. 42nd Session ISI, pp. 69--99, 1979.

....obtain new packet loss rate processes with a numerically more suitable time scale. For example, we created a loss rate process in which each sample represents the number of loss packets over 1,000 ms. We then apply well known Hurst parameter estimators [9] such as variance time and R S analysis [10], to test the presence of LRD and to estimate Hurst parameters. Estimated Hurst parameters for various scenarios are given in Tables 2 4. As shown in Tables 2 4, all estimated Hurst parameters are in the range [0.5, 1] This indicates packet loss process is LRD over time scales coarser than ....

B. B. Mandelbrot and M. S. Taqqu, "Robust R/S Analysis of Long Run Serial Correlation, " Proc. 42nd Session Int. Statistical Inst., Manila, December 1979, pp. 1--37.

....algorithms and, in Section 6, provide our conclusions. 2. Self similar processes In this section we define self similar processes and describe their main properties. It is only a brief outline and, for a more detailed presentation, the reader is referred to overview papers on selfsimilarity, like [14 17] and the references therein. 2.1 Definition and properties Let Y n ( be a discrete time arrival process. Let us define as Timescale of order m for the process Y n ( the timescale obtained from the original timescale, in which the Time Unit (TU) is the time slot, by aggregating ....

B. B. Mandelbrot, M. S. Taqqu, "Robust R/S Analysis of Long Run Serial Correlation", Proc. 42nd Session ISI, 1979, pp. 69-99.

....For ARMA and other short memory processes, the values of Q(n,q) converge to n J with J = 1 2. The parameter J is called the Hurst exponent and is related to the longmemory parameter d discussed above by J = d 1 2. Mandelbrot and co workers proved in a series of papers (see, for instance, Mandelbrot and Taqqu 1979) that when J 1 2, a process has long memory. Various methods can be used in R S analysis to estimate the J. A natural estimate for a series of length n is simply J = log Q(n,q) log n . 5) No distributional results are currently available for this estimate of J. 5 Another method of ....

Mandelbrot, B. and Taqqu, M. S. (1979): "Robust R/S analysis of long-run serial correlation ", Proceedings of the 42nd Session of the International Statistical Institute, Manila, Bulletin of the I.S.I., vol. 48, 2, 69--104.

....in many other traffic traces, as, for example, in Transport Control Protocol (TCP) and Motion Pictures Experts Group (MPEG) video traffic. An important characteristic of self similar traffic is its longrange dependence, i.e. the existence of correlation over a broad range of time scales [3, 4]. Until now, most of the network traffic measurements were performed on wired networks. The question arises whether the traffic in wireless data networks exhibits self similar behavior as well. If so, it is important to determine if this traffic characteristic affects the provisioning and ....

B. B. Mandelbrot and M. S. Taqqu, "Robust R/S analysis of long run serial correlation," 42nd Session of the International Statistical Institute , Manila, pp. 1-37, Dec. 1979.

.... Stochastic process with an autocorrelation structure of the form (9) are often viewed as finite approximations of a continuous sum of Gauss Markov processes; these are often interpreted as suggesting the presence of a multilevel hierarchy of underlying mechanisms which give rise to self similarity [73]. Some physical examples may be found in references cited by [16] In general, however, it is very difficult to demonstrate the physical existence of such multilevel hierarchies, or to relate extant mechanisms to self similar behavior. Consequently, formal mathematical models have been devised to ....

Mandelbrot, B.B. and Taqqu, M.S., "Robust R/S Analysis of Long Run Serial Correlation ", Proc. 42nd Session ISI, vol. XLVIII, Book 2 (1979), 69--99.

....and other short memory processes, the values of R(n) S(n,q) converge to n J with J = 1 2. The parameter J is called the Hurst exponent and is related to the long memory parameter d discussed above by J = d 1 2. Mandelbrot and co workers proved in a series of papers (see, for instance, Mandelbrot and Taqqu 1979) that when J 1 2, a process has longmemory. Various methods can be used in R S analysis to estimate the J. A natural estimate for a series of length n is simply J = log(R(n) S(n) log n . 5) No distributional results are currently available for this estimate of J. Another method of ....

Mandelbrot, Benoit B. and Taqqu, Murad S. (1979). "Robust R/S analysis of long-run serial correlation", Proceedings of the 42nd Session of the International Statistical Institute, Manila, Bulletin of the I.S.I., vol. 48, 2, 69--104.

....follows a power law [HURS51] i.e. E Theta R(n) S(n) n H ; as n 1; 2) with typical H values of around 0.7. Others have since shown that (2) holds for short range dependent processes with H = 0:5 [FELL51, MAND68] and for increment processes of selfsimilar models, where 0:5 H 1 [MAND79]. When working with empirical data, a practical implementation of the R=S analysis has been proposed by [MAND69a] see also [MAND79] and consists of plotting R(n) S(n) versus n, for different lags n and for different partitions of the observations. For our video trace, the resulting data is ....

.... since shown that (2) holds for short range dependent processes with H = 0:5 [FELL51, MAND68] and for increment processes of selfsimilar models, where 0:5 H 1 [MAND79] When working with empirical data, a practical implementation of the R=S analysis has been proposed by [MAND69a] see also [MAND79]) and consists of plotting R(n) S(n) versus n, for different lags n and for different partitions of the observations. For our video trace, the resulting data is plotted in a Pox diagram of R=S in Fig. 12. H can be measured ideally as the asymptotic slope of a straight line. Using the points ....

B. B. Mandelbrot and M. S. Taqqu, "Robust R/S Analysis of Long Run Serial Correlation", In Proc. 42nd Session ISI, Vol. XLVIII, Book 2, pp. 69--99, 1979.

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B. B. Mandelbrot, M. S. Taqqu, "Robust R/S Analysis of Long Run Serial Correlation", Proc. 42nd Session ISI, vol. XLVIII, Book 2, 69-99, 1979.

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