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Noise is a result of stochastic processes that originate from quantum or classical sources. Higher-order cumulants of the probability distribution underlying the stochastic events are believed to contain details that characterize the correlations within a given noise source and its interaction with the environment, but they are often difficult to measure. Here we report measurements of the transient cumulants ⟨⟨n[supm]⟩⟩ of the number n of passed charges to very high orders (up to m = 15) for electron transport through a quantum dot. For large m, the cumulants display striking oscillations as functions of measurement time with magnitudes that grow factonally with m. Using mathematical properties of high-order derivatives in the complex plane we show that the oscillations of the cumulants in fact constitute a universal phenomenon, appearing as functions of almost any parameter, including time in the transient regime. These ubiquitous oscillations and the factorial growth are system-independent and our theory provides a unified interpretation of previous theoretical studies of high-order cumulants as well as our new experimental data. [ABSTRACT FROM AUTHOR]