Multifractal detrended fluctuation analysis of sunspot time series

Abstract

We use multifractal detrended fluctuation analysis (MF-DFA), to See query 1\nstudy sunspot number fluctuations. The result of the MF-DFA shows that there\nare three crossover timescales in the fluctuation function. We discuss how the\nexistence of the crossover timescales is related to a sinusoidal trend. Using\nFourier detrended fluctuation analysis, the sinusoidal trend is eliminated. The\nHurst exponent of the time series without the sinusoidal trend is $0.12\\pm\n0.01$. Also we find that these fluctuations have multifractal nature. Comparing\nthe MF-DFA results for the remaining data set to those for shuffled and\nsurrogate series, we conclude that its multifractal nature is almost entirely\ndue to long range correlations.\n