The main objective of this monograph is to investigate the stochasticity of the approximately 11-year cycle of the sunspot series (1749-2024), known as the Schwabe cycle. To achieve this, we employed Fourier Analysis (FA), Wavelet Analysis (WA), and structural models for time series. Initially, we performed a spectral analysis using FA on the sunspot series divided into three distinct segments (1749-1840, 1841-1932, and 1933-2024), confirming the temporal variability of both the amplitude and period of the cycle across these segments. Next, through the scalogram of the sunspot series obtained via WA, we visually observed the evolution of the series’ frequencies and amplitudes over time. Finally, we modeled the sunspot series using Harvey’s structural model [10], where the series is decomposed into stochastic trend and cycle components. This model was then used to forecast the series for the period from 2013 to 2024. Its predictive accuracy was compared with another model that had the same stochastic trend but a deterministic cycle. The accuracy metrics used (RMSE and MAE) indicated the superior predictive performance of the model with a stochastic cycle. This result reinforces the evidence of the stochastic nature of the 11-year cycle in the sunspot series.