Empirical study of the scaling behavior of the amplitude-frequency distribution of the Hilbert-Huang transform and its application in sunspot time series analysis

► We empirically deduce a new scaling relationship in the Hilbert-Huang transform. ► We deduce this relationship from marginal integration. ► We numerically show the equivalence of the relationship from two angles. ► Incomplete removal of periodic trends leads to a Hurst exponent of sunspots of 0.12.