The Hurst effect is a presumed and unexpected behavior of geoastrophysical time series by which these time series have persistence or “memory.” The application of Hurst analysis to monthly sunspot numbers [B. B. Mandelbrot and J. R. Wallis, Water Resour. Res. 5, 321 (1969)] yielded a Hurst exponent $H=0.86\mathrm{}\pm 0.05,$ suggesting that solar activity shows persistence and that the underlying responsible mechanism can guarantee a positive correlation of solar activity during long time lapses, raising, at the same time, the possibility of the existence of long-term memory in solar activity. More recently, radiocarbon data have been used for a similar study [A. Ruzmaikin, J. Feynmann, and P. Robinson, Sol. Phys. 149, 395 (1994)] resulting in a constant value $H=0.84\mathrm{}$ between 100 and 3000 years, which indicates persistence of solar activity in such time scales. Furthermore, Mount Wilson rotation measurements have also been analyzed in the same way [R. W. Komm, Sol. Phys. 156, 17 (1996)] and the results indicate that temporal variations of solar rotation on time scales shorter than the 11-year cycle are caused by a stochastic process which is characterized by persistence. Here, we have followed the scale of fluctuation approach to show that there is no incontrovertible evidence for the presence of the Hurst effect in sunspot areas and, therefore, that there is no proof of the existence of long-term memory in solar activity.

• Received 18 May 1998

DOI:https://doi.org/10.1103/PhysRevE.58.5650