On the statistical stability of solar cyclicity

A form function for the 11-year solar-activity cycles is introduced for an interval equal to the duration of the cycles, with allowance for the asymmetry of the latter. A mathematical model is proposed to describe the time structure of solar cyclicity. A method and algorithm for optimal estimation (in the sense of the minimum of the root-mean-square deviation) of its parameters are described. The statistical correlation of parameters of 11 year cycles is discussed and the stability of their fine structure is illustrated. The residual dispersion is calculated with allowance for all 20 cycles of the Zurich numbering (after subtracting from the initial data their approximated values). Attention is drawn to the uniformity of its variation from cycle to cycle as a test of the statistical stability of the shape of the latter. The sources of disruption of the indicated uniformity for monthly average observed Wolf numbers are calculated and ways of eliminating them are indicated. It is concluded that the statistical stability of the shape of the 11-year solar-activity cycles is real to within the variation of their asymmetry.