An early prediction of 25th solar cycle using Hurst exponent

The analysis of long memory processes in solar activity, space weather and other geophysical phenomena has been a major issue even after the availability of enough data. We have examined the data of various solar parameters like sunspot numbers, 10.7 cm radio flux, solar magnetic field, proton flux and Alfven Mach number observed for the year 1976–2016. We have done the statistical test for persistence of solar activity based on the value of Hurst exponent (H\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$H$\end{document}) which is one of the most classical applied methods known as rescaled range analysis. We have discussed the efficiency of this methodology as well as prediction content for next solar cycle based on long term memory. In the present study, Hurst exponent analysis has been used to investigate the persistence of above mentioned (five) solar activity parameters and a simplex projection analysis has been used to predict the ascension time and the maximum number of counts for 25th solar cycle. For available dataset of the year 1976–2016, we have calculated H=0.86\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$H = 0.86$\end{document} and 0.82 for sunspot number and 10.7 cm radio flux respectively. Further we have calculated maximum number of counts for sunspot numbers and F10.7 cm index as 102.8±24.6\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$102.8\pm 24.6$\end{document} and 137.25±8.9\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$137.25\pm 8.9$\end{document} respectively. Using the simplex projection analysis, we have forecasted that the solar cycle 25th would start in the year 2021 (January) and would last up to the year 2031 (September) with its maxima in June 2024.