Information Entropy Of Complex Time Series And Its Application

In recent years,more and more attention has been paid to the research related to the information entropy of time series.Generally,complex time series generated by complex systems show statistical characteristics such as irregularity,randomness,fractal and nonlinearity.Multiple analysis methods based on information entropy provide a new way to study these statistical characteristics of complex time series.This paper proposes and studies the time series analysis methods related to information entropy,and simulates the feasibility and stability of these methods through various models.Finally,the paper makes an empirical demonstration with a variety of financial time series and traffic system series.In this paper,four methods in the field of information entropy are proposed to study the irregularity and correlation of complex time series.The first research method is the transfer entropy of nonlinear transformation.In this paper,the transfer entropy is extended to five kinds of transfer entropy of nonlinear transformation with practical financial significance.This paper explores the information transmission relationship and mutual influence relationship among multiple financial stock markets under nonlinear transformation.The results show that four of the five nonlinear transformations studied in this paper increase the transfer entropy,which provides a strong support for the correlation study of time series.The second method is based on the improvement of irreversibility measurement of viewable time series.In this method,the data space is reconstructed by multi-dimensional coding of the forward and backward access degrees of the sequence,and the irreversibility of the complex time series is measured by the kullback-leibler(KL)divergence.The partial model and empirical results show that the irreversibility of the time series will reach its peak when the encoding scale is 3.The third method is the multi-scale weighted distribution entropy method.This method enhances the effect of considering the degree of dispersion of data set in measuring distribution entropy by means of variance weighting method.This can make full use of the information contained in the data and explore the weighted distribution entropy from the perspective of multi-scale data space.The results show that the weighted distribution entropy decreases with the increase of the embedding scale of data dimension.The fourth method is manifold learning based on kernel function and generalized information measure.Firstly,the performance evaluation data sets of various industries are processed by kernel function,and the non-separable data sets with hioh dimensions are transformed into linearly separable data sets.Then,the information distance is measured by generalized KL divergence to obtain the relational measurement matrix.Finally,the purpose of manifold dimension reduction is achieved by extracting matrix features.