The analysis and forecasting of the Wolf sunspot numbers

Abstract

The yearly mean Wolf sunspot numbers from 1700 to 1964 are frequency analysed using techniques developed previously for shortperiod variable stars. The 14 statistically significant periodicities revealed by the analysis are shown to be the consequence of the amplitude and phase modulation of the main 11-yr periodicity by two long periods of 90 and 55 yr. A correlation is found between the amplitude and the phase variations, which, if it held during the Maunder Minimum, explains the irregularity of the recorded times of maxima during that interval. Seasonally stationary autoregressive models of the sunspot numbers are constructed. These models are found to show considerable improvement over previous autoregressive models by comparison of forecasts in an out of sample interval. The models are used to make forecasts for the current sunspot cycle.