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.

最近提出了递归空隙性来检测不同时间尺度上的动态状态转换。在本文中，我们结合建议的分布矩并引入多重分形递归空隙来挖掘相空间中丰富的轨迹信息。通过考虑广义矩，它提供了增强的测量来解释不同尺度的重现图中黑色像素的差异。数值模拟证明，该方法能够区分不同类型的时间序列，并提供对随机序列、混沌映射和序列污染干扰分量等固有特征的进一步了解。在现实应用中，它在量化金融时间序列的微妙结构变化方面表现良好。此外，令人感兴趣的是，证实波纹信号在重现图方面比正常信号拥有更生动的异质性信息。