Additive as well as multiplicative noise may occur when acoustic waves propagate through the ocean. Second-order spectral methods fail to retrieve frequencies of such random amplitude modulated harmonic time series, especially when the multiplicative noise is broadband. An existing fourth-order method assumes real Gaussian multiplicative and additive noise. A novel approach is proved herein to impose no constraints on the distribution or the color of the disturbances. It relies on fourth-order special cumulant or moment slices. In particular, the fourth-order moment spectrum is shown to offer computational advantages. Extension to multicomponent models and generalizations to alternative higher order moments are also provided. Simulations corroborate the theoretical results.