Comment on “The Hurst exponent and long-time correlation” [Phys. Plasmas 7, 1181 (2000)]

k g The paper ‘‘The Hurst exponent and long-time corre tion’’ by G. Wang et al. reaches a very surprising conclu sion. The authors state: ‘‘It @ he fact thatH is well above 0.5# is found to be connected with short-time correlations These results suggest that the R/S method is not appropriate for evaluating long-time correlations in fusion devices This conclusion is surprising in several respects. First, R/S method has been applied with success in many fields a tool for investigating long-range dependencies. The r tionship between a high value of the Hurst parameter, H, and self-affinity ~i.e., long-term memory or long-range depe dency! has been established in a large number publications. 3 It is difficult to understand how and why th method should lead to different conclusions in the particu case of probe data from Tore Supra. Second, their conclu does not answer the question of why and how short-ra correlations should appear as long-range dependencies nally, the statement that this failure is generic to fusion vices is also surprising. The test of theR/S method suggested by the authors reasonable. It is an extension of the standard test of shuffling, which we ourselves have used in testing our R/S algorithm. The test consists of subdividing the data set in blocks of lengthN and shuffling the blocks. This shoul decorrelate any scales longer than N. One must, however, be careful when choosing a range of time lags over which th H exponent is determined. There is no discussion of this p in the paper, nor do the authors give any details about ranges they have used. The range should be such tha R/S trace has a well-defined power scaling, it should inclu at least a decade of lag values, and its lower end should b lags that are large compared to the size of the blocks N. Also, one should bear in mind that the high range of values of R/S has poor statistics~is calculated from few independent es mates!, so that the accuracy of the R/S values decreases wit increasing time lag. It is difficult to give a more detaile numerical prescription for the calculation of H. One should