MEASURING STRUCTURAL CHANGES OF RECURRENCE PATTERNS IN MULTIFRACTAL AND MULTISCALE ASPECTS BY GENERALIZED RECURRENCE LACUNARITY

Abstract

Recurrence lacunarity has been recently proposed to detect dynamical state transitions over various temporal scales. In this paper, we combine suggested distribution moments and introduce multifractal recurrence lacunarity to unearth rich information of trajectories in phase space. By considering generalized moments, it provides an enhanced measurement to account for differences of black pixels in the recurrence plot at various scales. Numerical simulations have proved that the proposed method is able to differentiate varying types of time series and provide further insights of inherent features including stochastic series, chaotic maps and series contaminated interference components. In real-world applications, it performs well on quantifying the subtle structural changes of financial time series. In addition, it is intriguing to confirm that corrugation signals possess much more vivid information of heterogeneity in terms of recurrence plots than normal ones.