Distortions in Periodicity Analysis of Blazars: The Impact of Flares

Blazars, a unique class of active galactic nuclei, exhibit highly variable emission across the electromagnetic spectrum. This variability frequently manifests as intense flaring events, sparking an ongoing debate in recent literature about whether these flares exhibit periodic behavior in certain sources. However, many blazars also show clear signs of stochastic, uncorrelated flares that do not follow a regular pattern. This paper explores how the presence of one such of these stochastic flares can distort an intrinsically periodic pattern of emission in blazars. Our results demonstrate that, depending on the specific circumstances, the deviations in significance and periods can exceed 100\%. Sometimes, these deviations can be so severe that they eliminate any evidence of a periodic pattern. These findings highlight the dramatic impact that flares can have on periodicity searches. To confront this challenge, we propose an innovative approach, the Singular Spectrum Analysis method, which appears more robust against the effects of flares. As an alternative solution, we also propose the sigma clipping technique to mitigate the impact of flares. This framework offers a valuable foundation for analyzing periodicity in similar astrophysical sources that are also subject to stochastic flaring events.