The Complexity Research Of Financial Time Series Based On Fuzzy Entropy

The financial markets are complex systems with fractal and chaotic structures with large-scale internal components.Financial data usually have the characteristics of nonlinear,non-stationary,long-range correlation,at the same time,because of the particularity of the financial system itself and its core and strategic position in the economic system,its complexity research of time series has more theoretical research value and practical application value.In recent years,fuzzy entropy as an important measure of time series complexity has attracted the attention of economic researchers and empirical researchers.In this paper,the Fuzzy entropy measure is improved from the angle of fractional order and multivariate to make it more suitable for nonlinear,non-stationary,short sequence length and complex financial time series with noise pollution.The validity and stability of the method are verified by artificial simulation data,compared with the traditional fuzzy entropy model,and the actual financial time series are analyzed by these methods.The empirical results show that our proposed method can not only effectively overcome the limitations of the original method in terms of the harsh relationship between time series length and mode vector,numerical degradation,large fluctuation,but also significantly distinguish different short-term financial time series.The specific organizational framework of this paper is as follows:In Chapter 1,the research background,purpose and significance of fuzzy entropy and time series complexity are combed,as well as the domestic and foreign research reviews,and the research framework of the full text is given.In Chapter 2,introduces the related theoretical knowledge of fuzzy entropy,as well as the basic theoretical knowledge of logarithmic return sequence,volatility sequence and so on in financial time series.In Chapter 3,fractional refined composite multiscale fuzzy entropy(FRCMFE)is proposed based on multiscale fuzzy entropy method combined with fractional calculus,refined and composite techniques.FRCMFE can obtain more sensitive and stable data analysis results,and we used it for the first time to study the complexity dynamics of the yield and volatility sequence of international stock indices.In Chapter 4,considering that real-world financial market data are usually multivariable.Multivariate entropy is a method to analyze the complexity of multichannel data,which has been applied to the detection of multichannel physiological data and environmental data,combining multivariate entropy with fractional calculus,multiscale and composite technique,a new developed complexity version refined composite multivariate multiscale fractional fuzzy entropy(RCmvMFFE)is proposed to explore and discriminate the complexity dynamics of the multichannel financial time series in different regions.RCmvMFFE is then compared with multivariate multiscale fuzzy entropy(mvMFE),refined composite multivariate multiscale fuzzy entropy(RCmvMFE)for simulation data verification.Finally,the empirical analysis shows that our proposed method can dig deeply and sensitively the market information hidden in the multichannel financial data,and to a certain extent,it can better distinguish the multichannel financial time series of different regions(Asia-pacific region,Europe region and Americas region)at home and abroad as well as different stages of development.In Chapter 5,this paper introduces the summary of the research results and innovation points,and the prospect of future research work.