The Refined Two-index Entropy And Recurrence Analysis Of Time Series

With the development and pervasive application of the science and technology,analysis of time series has been a hot topic of interdisciplinary research.The complexity and recurrence have gradually become crucial methods to recover the evolvement of real world.By analyzing the complexity and recurrence of time series,we can find the operation of system,and then execute forecasting.This paper focuses on these two properties of time series and proposes two new models and analysis perspectives.One of these is a two-index entropy model and we find the new two-index entropy is applicable to measure the complexity of wide range of systems in the terms of randomness and fluctuation range.Another one is a recurrence quantification analysis mode,which is based on singular value deccmposition,named PSVP.After building these models,this paper chooses financial time series,traffic flow and physiological data as testing time series.This paper measures the complexity of non-stationary time series based on the entropy theories.During the past several decades,various kinds of entropy model have been proposed,like Boltzmann-Gibbs entropy,Sample entropy and Permutation entropy.Based on the famous q entropy and ? entropy,we propose a refined two-index entropy to measure the complexity of non-stationary time series.The refined entropy model widens the range of entropy measure.Based on the two-index entropy,this paper sets index q and ? as variable respectively and present multi-scaling theory of this two-index entropy.Then we take 7 real series from the finance markets around the world as the real test.We find the refined two-index can measure the complexity of non-stationary time series efficiently and classify these finance markets on account of the various complexities.Recurrence plot has turned into a powerful tool in many different sciences in the last three decades.To quantify the complexity and structure of RP,recurrence quantification analysis(RQA)has been developed based on the measures of recurrence density,diagonal lines,vertical lines and horizontal lines.This paper studies the RP based on singular value decomposition which is a new perspective of RP study.Principal singular value proportion(PSVP)will be proposed as one new RQA measure and bigger PSVP means higher complexity for one system.In contrast,smaller PSVP reflects a regular and stable system.Considering the advantage of this method in detecting the complexity and periodicity of systems,several simulation and real data experiments are chosen to examine the performance of this new RQA.