Some Studies On The Large Deviation Spectrum And Complexity Of Financial Time Series

In many complex dynamic systems,financial system is closely connected with our life,and people pay more and more attention to this system.The research of financial system is often attributed to the research of financial time series.In recent years,a series of analytical techniques have been continuously developed and improved.On this basis,this paper further improves some existing models.The models involved include large deviations spectrum estimation,generalized entropy plane,recurrence quantification analysis,etc.We select some representative artificial simulation data,analyze the advantages of the improved model compared with the original model,and verify the robustness of the model.Besides,In addition,the proposed model is used to do a simple empirical analysis of financial stock index data.We study the regional differences and other characteristics of different stocks.Specifically,the main contents of this paper are as follows:(1)We propose to use higher-order moments(e.g.,skewness and kurtosis)instead of the original oscillation-based roughness exponent to study the multifractal characteristics of large deviation spectrum.When using higher-order moments as a new roughness exponent,the traditional normalization procedure of signals will fail.In order to solve this problem,a new standardization method is proposed.Generated simulation data and financial time series are used to verify our model,and we compare the results with another commonly used multifractal spectrum method,Legendre spectrum.It is found that our large deviation spectrum method overcomes the limitations of Legendre spectrum and reveals the information that remains hidden with Legendre spectrum.Besides,we also discuss the scaling /non-scaling criterion of the method.The results show that the financial time series does not have good scale invariance.(2)We propose a new generalized entropy plane model based on the large deviation spectrum theory and the complexity-entropy causality plane analysis.This model combines the characteristics of the two methods,uses the roughness exponent and scale function involved in large deviation spectrum theory to study the relationship between them.It can describe the complexity of the system in two-dimensional plane.Simulated data and financial stock market index series are applied to the proposed model,and we discuss the impact of the parameters on the results in detail.The model can distinguish different time series and provide abundant dynamical properties of complex systems.(3)We propose another generalized entropy plane model.In this model,permutation entropy and weighted permutation entropy are used to measure the complexity of dynamic system.We study the relationship between the two kinds of entropy with multi-scale analysis.The results show that the permutation entropy and weighted permutation entropy have good linear correlation in the sense of multi-scale.We also use the financial time series to study,and confirm that this good linear relationship also exists in the financial system.At the same time,we propose to use their linear regression slopes as a new discriminant statistic to test the nonlinear characteristics of time series,and obtain good results.(4)We propose an adaptive method for threshold of recurrence quantification analysis.This method can describe the complexity and structural characteristics better.Our method needs to combine cumulative histogram method to achieve the effect of adaptive threshold selection.In order to reduce the complexity of cumulative histogram calculation,we introduce a symbolic representation of time series: symbolic aggregate approximation.The model is applied to generate simulated data and compared with the results obtained by the original one.Our model shows robustness to the length,noise and sampling frequency of the time series.We also apply the model to the financial stock market and get some interesting results.