Determining the maximum of solar cycle 25 with a memory modulated white noise

Abstract The exact determination of the solar maximum of a solar cycle before it occurs remains an open problem in solar physics. Using a memory modulated white noise framework, a procedure is presented to determine the still unknown solar maximum of solar cycle 25. We investigate the first thirty months of each of the past 24 solar cycles from 1755 to 2019 using a second order structure function derived from white noise analysis. Specifically, the mean square deviation (MSD) of the fluctuating monthly sunspot numbers for the first 30 months of a solar cycle is matched with the theoretical MSD to obtain a value for the memory parameter <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>μ</mml:mi> <mml:mo>.</mml:mo> </mml:math> By similarly determining the value of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>μ</mml:mi> </mml:math> for the first 30 months of solar cycle 25, a forecast is made for its solar maximum.