Wolf Numbers and Statistics

AbstractThe article proposes a unified method for statistical analysis of random processes that combines leading frequency detection, singular spectrum analysis (SSA), and Monte Carlo testing. We introduce a mathematical transformation to extract dominant components, formulate statistical criteria to distinguish randomness from regularity, and develop recursive probabilistic forecasting procedures. The Monte Carlo framework is used to assess the statistical significance of SSA components, while the recursive scheme produces probabilistic short-term forecasts. The method is validated on the sunspot (Wolf) number series: SSA reveals persistent oscillatory modes, Monte Carlo tests confirm their significance, and probabilistic forecasts outperform baseline models in short-term predictive skill. Our analysis also indicates that, over the observational record, Wolf numbers have increased somewhat faster than theoretical models predict.Wolf Numbers and Statistics, 2026, msc: 85A99, 62A99 Key words: Wolf numbers, singular spectrum analysis, Monte-Carlo criterion, prediction of randomprocesses, separation of law and chance, Maunder Minimum, mathcad 15, SSA method, probabilisticrecursive prediction.