Analysis Of Local Irreversibility And Volatility Of Time Series

In recent years,more and more attention has been paid to the study of the irreversibility and volatility of time series of complex systems.The irreversibility study mainly involves the variability of signal statistical characteristics under the operation of time reversal,and the volatility analysis mainly involves the volatility study of one-dimensional time series and the amount of information transmission between two-dimensional time series.But so far,the local irreversibility study of time series is lacking,and the common points and difference points of the different volatility analysis methods of time series are not clear enough.In addition,the combination of fractional scale and entropy needs to be further explored.Therefore,it is necessary to study the local irreversibility and volatility characteristics of different time series.The main research contents of this I paper are as follows:(1)This paper provides several volatility analysis measures based on limited time series by means of symbolic algorithm: topological entropy,geometric entropy,relative entropy and Shannon entropy based on singular value decomposition;In addition,this paper further explores the characteristics of the number of missing patterns over time scale and time delay.The advantages of these measures in studying the volatility of time series are verified through many experiments.(2)In order to solve the problem of local irreversibility of time series,this paper proposes a multi-scale method based on segmentation and combines it with a variety of irreversible measures,effectively analyzes the local irreversibility variation characteristics of simulation data,financial data and physiological data,and its relationship with the overall irreversibility.(3)This paper applies the idea of fractional theory,redefines the empirical mode decomposition energy entropy,and constructs the fractional distribution entropy based on the missing pattern.In the experimental part,this paper selects the analog time series and the electrocardiogram signal,and finds that the fractional entropy can show better characteristics in the volatility analysis of the dynamical system compared with the traditional integer entropy.