Complexity Analysis Of Time Series Based On Information Entropy Theory

This paper mainly focuses on the theory of information entropy,and applies it to measure the complexity of financial system.In view of the inherent defects of the traditional model,this paper proposes improved methods based on the algorithm principle to better extract and quantify the key information contained in the sequence.At the same time,considering the various scenarios encountered in real applications,the model is improved to be closer to the reality and measure the real-world complex systems with a higher accuracy.Firstly,based on the theory of cumulative residual entropy and distribution entropy,this paper proposes the cumulative residual distribution entropy(CRDE).The new model makes full use of the known information,including not only the information of probability,but also the information about the value of random variables,and makes full use of the potential inherent information of vector-to-vector distance in the state space.In this paper,the cumulative residual distribution entropy model is extended to the fractional order.The generalized fractional cumulative residual distribution entropy can better capture the tiny evolution of signal data,which is more advantageous for studying the dynamic characteristics of complex systems.The empirical analysis of simulated data and stock market data shows that the CRDE has low sensitivity to its own parameters,can better reflect the sequence complexity and risk to a certain extent,and the performance of the model is better when it is extended to fractional order.Secondly,this paper deeply studies the dispersion entropy,and proposes the generalized fractional order multiscale dispersion entropy(GMDE)and the generalized fractional order refined composite multiscale dispersion entropy(GRCMDE).In the new model,normal cumulative distribution function and linear mapping are used to deal with the original time series in advance.The new models take the amplitude value information of the sequence itself into consideration,and can make better use of some key information in the sequence,which have a higher stability and accuracy.The empirical analysis part verified its effectiveness by applying the model to simulated data and stock market data,and selected the main stock index sequences of developed and developing countries to study the complexity of the financial system and its characteristics of multiple time scales.The results show that DE,MDE,RCMDE,GMDE and GRCMDE can detect the inherent nature of financial time series and distinguish the complexity of financial markets in different countries.Then,this paper continues to discuss the content of complexity measurement of multivariate time series,proposes dual-embedded dimensional multivariate multiscale dispersion entropy(mvMDE),and generalize the new model to fractional order(GmvMDE).The mvMDE and GmvMDE simultaneously consider the cross-correlation between multiple channels,and they provide a dynamic complexity measure for measuring the multivariable data observed in one system.We introduce dual embedded dimensions to construct subsequences,which makes the model more flexible and applicable to a variety of application scenarios.Through empirical analysis of simulated data and stock market data,this paper verifies that both mvMDE and GmvMDE can effectively measure and distinguish the sequence complexity,and show its differences in the temporal structure.Finally,this paper innovatively measures system complexity from a systematic perspective,and proposes the multiscale system dispersion entropy(MSDE)and its fractional order form(GMSDE).Using the vector-to-vector distance quantization method,the relationship between individuals in the system can be better extracted,and the systemic complexity of financial portfolio can be measured from the time dimension and the space dimension simultaneously.The empirical analysis based on different financial portfolios of the same industry and different industries in Chinese stock market shows that MSDE and GMSDE can accurately capture the structural information in the system and effectively distinguish the complexity of financial portfolios,and the model performance is significantly better than the traditional models.The concept of system entropy is of great significance for quantitative analysis of financial markets and optimization of investment portfolio allocation.