Solar Activity Spikes: A Comparative Analysis of Monthly Smoothed and Unsmoothed Sunspot Numbers

This work investigates the differences between the monthly and 13-month smoothed sunspot numbers since 1749, using data from sunspot number (version 2). The distribution of the differences is centered near zero, with 74% of all values lying between −20 and +20, and only 1% exceeding ±70. Positive and negative differences are nearly balanced in total number, although the distribution of the monthly differences is moderately asymmetric (skewness = −0.55) and high kurtosis (>3), confirming leptokurtic behavior with sharper peak around zero and heavier tails than a Gaussian distribution. Spikes, defined in each tail using the 95th and 5th percentile, occurred in nearly all solar cycles studied, predominantly around solar cycle maxima and in cycles with higher solar activity. Moreover, the five most extreme cases with a difference of more than 100 occur in five solar cycles, ranging from below to above average. Additionally, we analyze the recent behavior of Solar Cycle 25. The significant increase in the monthly sunspot number in August 2024 (it reached 216, the highest since 2001) raised questions about the potential future intensity of Solar Cycle 25. As the sunspot number series evolved, this difference between the maximum monthly and 13-month smoothed series decreased to 55.1 (with data through October 2025), placing Solar Cycle 25 within the historical relationship between maximum monthly and 13-month smoothed sunspot number, and the largest monthly deviations. Our results show that spikes are a recurrent feature of solar activity and can provide useful diagnostics for shorter-term solar cycle variability.