Modeling Fluctuations in Daily Sunspot Numbers Using White Noise Analysis

In this work, we model the fluctuations in daily sunspot numbers, denoted by X(t), as a modulated Brownian motion using a white noise analysis framework. We analyze data from the past 15 solar cycles with a complete record (Solar Cycles 10 to 24) and characterize the deviations in X(t) over timescales from 1 to ∼ 2000 days. We demonstrate that the observations can be adequately matched by a white noise model with 3 parameters: an amplitude parameter N, a decay parameter β, and a memory parameter μ. By matching the model with the observed time series from individual solar cycles, we are able to characterize the properties of each as well as potentially detect evolution in the stochastic component of the sunspot time series over the last ∼100 years. The approach followed here can also be readily applied to other indices of solar activity.