Characterization of irregular cyclicities in heavy-tailed data

The statistical characterization of heavy-tailed data with hidden irregular periodicities is introduced. Specifically, processes generated by the interaction of random phenomena with heavy-tailed distribution and almost-periodic phenomena with possibly irregular or disturbed peridicities are characterized in terms of fractional lower-order moments. For this wide class of processes, fractional lower-order moments are expressed as the superposition of amplitude- and angle-modulated sine waves. The model introduced in the paper extends the previously introduced one for heavy-tailed almost cyclostationary (ACS) processes to the case of irregular periodicities. Moreover, it introduces for the class of the oscillatory ACS processes a characterization in terms of fractional lower-order moments. For the new class, the problem of statistical function estimation is addressed. The effectiveness of the proposed methodology is corroborated by the analysis of simulated alpha-stable time-warped ACS processes and of real acoustic helicopter data.