Multifractal analysis of sunspot time series: the effects of the 11-year cycle and Fourier truncation

Multifractal theory provides an elegant statistical characterization of many complex dynamical variations in Nature and engineering. It is conceivable that it may enrich characterization of the sun’s magnetic activity and its dynamical modeling. Recently, on applying Fourier truncation to remove the 11-year cycle and carrying out multifractal detrended fluctuation analysis of the filtered sunspot time series, Movahed et al reported that sunspot data are characterized by multifractal scaling laws with the exponent for the second-order moment, h(2), being 1.12. Moreover, they think the filtered sunspot data are like a fractional Brownian motion process with anti-persistent long-range correlations characterized by the Hurst parameter H = h(2) − 1 = 0.12. By designing an adaptive detrending algorithm and critically assessing the effectiveness of Fourier truncation in eliminating the 11-year cycle, we show that the values of the fractal scaling exponents obtained by Movahed et al are artifacts of the filtering algorithm that they used. Instead, sunspot data with the 11-year cycle properly filtered are characterized by a different type of multifractal with persistent longrange correlations characterized by H ≈ 0.74.