Statistical analysis of the 11-year and the 80-year solar cycles

The time dependences of Wolf's number in the available 11-year cycles of solar activity by use of the method of the linear two-parameter regression analysis and of its subsequent extension are calculated. The parameters of the cycles are determined and then are compared. The period of the long (the 80-year) solar cycle corresponding to the maximal total correlation coefficient and to the minimal standard deviation has been further numerically determined. Thereby the parameters of the long cycles of solar activity characterized by Wolf's numbers are calculated. The long solar cycle with the period 82.8-84.8 years has been proved to be statistically significant, which is in good agreement with the period of the long cycle, i. e. about 80 years. On the basis of the data on smoothed maxima of Wolf's numbers in individual 11-year solar cycles and by use of the method mentioned above, the existence of the long solar cycles with the period 87.2 and 81.8 years has been statistically proved as well