Modeling and prediction of sunspot cycles

Solar activity, as indexed by sunspots, has a cycle of length varying from about 9 to 13 years. Statisticians have fitted several models to predict sunspot numbers one year ahead. We instead focus on predicting the magnitudes of the next cycle maximum, the next cycle minimum, the time from the initial minimum of a cycle to its maximum, called the rise time, and the time from a cycle maximum to the next cycle minimum, called the fall time. The predictions are based on sunspot numbers just far enough into a new cycle to establish that a cycle has started. We propose parsimonious regression models for the maximum and rise time. For the fall time and minimum we propose crude models, based on the sample means and variances for all past cycles. We compare our models to simulation results for many models we found in the literature including autoregressive (AR) models, subset AR (SAR) models, and related nonlinear models including a threshold AR model, transformed by squaring (TTAR model), a bilinear model, a so-called ASTAR model, and a neural network (CNAR) model. We also consider a model proposed by solar physicists, based on a functional form for cycles.