An econometric investigation of the sunspot number record since the year 1700 and its prediction into the 22nd century

Abstract

Solar activity, as measured by the yearly revisited time series of sunspot numbers (SSN) for the period 1700–2014 (Clette et al., 2014), undergoes in this paper a triple statistical and econometric checkup. The conclusions are that the SSN sequence: (1) is best modeled as a signal that features nonlinearity in mean and variance, long memory, mean reversion, ‘threshold’ symmetry, and stationarity; (2) is best described as a discrete damped harmonic oscillator which linearly approximates the flux-transport dynamo model; (3) its prediction well into the 22nd century testifies of a substantial fall of the SSN centered around the year 2030. In addition, the first and last Gleissberg cycles show almost the same peak number and height during the period considered, yet the former slightly prevails when measured by means of the estimated smoother. All of these conclusions are achieved by making use of modern tools developed in the field of Financial Econometrics and of two new proposed procedures for signal smoothing and prediction.