Robust method for periodicity detection and characterization of irregular cyclical series in terms of embedded periodic components

A method for periodicity detection is proposed where unlike available methods a periodic component is characterized in terms of three basic periodicity attributes: the periodicity (or period length), the periodic pattern, and the scaling factors associated with the successive nearly repetitive segments. A scheme is proposed for subsequent successive detection and extraction of such (hidden) periodic or nearly periodic components constituting an irregular cyclical series. To our knowledge, the proposed decomposition is much more powerful in terms of information content and robustness than the presently available tools based on Fourier decomposition. Through the analysis of a variety of natural, experimental, and simulated data series, it is shown that the features of the periodicity attributes of the embedded periodic components can lead to a meaningful characterization of an irregular series in a new perspective.