Application Of Information Categorization And Information Entropy In Time Series Analysis

In recently,analysis of time series based on information entropy has attracted more and more attention,and has been widely used in many fields,such as physiology,transportation and finance and so on.In this paper,our research objects are financial time series.We propose several statistical methods to classify these time series and analyze the correlations and complexity between the time series.The first method is analysis of time series through information categorization.We study dissimilarity between pairs of sequences by defining a new metric to obtain their spatial configurations,and then applying the method into analyzing time irreversibility of sequences,to provide a new indicator for studying the financial stability.The second approach is promoting one time series to two time series,which means that we analyze the complexity between two cross-sequences,and extend the distribution entropy to the concept of multiscale.We analyze the relationship between the multiscale cross-distribution entropy(MCDE)and the parameters and correlations between the time series.The third method is that we introduce the Shannon-Fisher entropy curves to classify the time series and investigate the complexity of time series.The last one is a complexity-entropy plane based on generalized fractional entropy model by extending the fractal order to Shannon entropy.On the one hand,we utlize this complexity-entropy plane to distinguish between chaotic time series and random time series.On the other hand,we could classify financial time series and compare the classification results with those obtained by the classical complexity-entropy plane.The main research contents of the paper are as follows:(1)We propose a new dissimilarity between pairs of sequences called information categorization method.We apply this method to multidimensional scaling(MDS)and analyzing time irreversibility.We firstly employ the MDS based on information categorization to analyze the artificial time series and financial time series,and obtain their spatial configurations.Moreover,we could also use this method to classify the time series.When applying the information categorization to time irreversibility,we investigate the relationship between the annualized volatility and time irreversibility of 33 American companies,and cluster the years by their levels of reversibility.(2)We propose a MCDE method that innovatively promotes one time series to two time series,which means we analyze the complexity between two cross-sequences,and extend the distribution entropy to the concept of multiscale.When applying the method into two kinds of model: ARFIMA model with Gaussian noise and ARFIMA model with non-Gaussian noise,we analyze the relationship between the MCDE and the parameters and the correlation analysis of time series.In addition,when applying the method into analyzing financial time series,we could classify financial time series and study the stabilies of financial stock indexes.(3)We propose the Shannon-Fisher entropy curves based on the distribution entropy method.We firstly apply it into ARFIMA model and Chebyshev map model to examine the effectiveness of the method.Then we utlize this method to analyze the volatility of financial time series and the corrections between the financial stock indexes.In addition,we could get the information on the classification of financial time series in the Shannon-Fisher curves plane,and compare the result of classification with the result obtained by the classical Shannon-Fisher curves.(4)We propose a complexity-entropy plane based on generalized fractional entropy model to study the relationship between the fractal dimension and generalized fractional entropy and statistical complexity from the point of view of phase space reconstruction.We analyze the relationship between the fractal dimension and the generalized fractional entropy and statistical complexity for different time series.Moreover,we use the proposed complexity-entropy plane to distinguish between chaotic sequences and random sequences,and also classify financial time series.