The Volatility Identification Of Financial Time Series:A Perspective Of Granule Complex Network

The volatility is one of essential characteristics of financial time series,which is vital for the knowledge acquisition from financial data.However,since the high noise and non-steady features,the volatility identification of financial time series is still a challenging problem.In this article,from a perspective of granule complex network,a novel approach is proposed to the study of this problem.Firstly,numeric time series are structured into information granules,where the segments of time series in each granule would own similar volatility features.Secondly,by using the transfer relations among granules,granule complex network is to be constructed,which intuitively describe the transfer processes among different volatility patterns.Thirdly,a novel community detection algorithm is applied to divide the granule complex networks,where granules with frequent mutual transfers would belong to the same granule community.Finally,Markov chain model is carried out to analyze the higher level of transfer processes among different granule communities,which would further describe the larger-scale transitions of volatility in overall financial time series.An empirical study of the proposed system is applied in the Shanghai stock index market,where volatility patterns of financial data can be effectively acquired and the corresponding transfer processes can be analyzed by means of the granule communities.Therefore,from the point of view of granular complex network,this paper analyzes the fluctuation law of financial time series,which can effectively solve the problem of high noise and non-steady of financial time series,and comprehensively analyze the volatility of financial time series from different dimensions.The contributions and innovations of this paper mainly include the following aspects:(1)The time series is granulated,and the time series with similar volatility patterns are clustered by using the method of fuzzy clustering.Each class is regarded as a different granule node,and the transfer between classes is regarded as a directed edge,and then the granular complex network is constructed.In granular complex networks,as nodes of networks,granules represent fluctuation patterns with similar characteristics,and weighted edges represent the transfer process of fluctuation patterns.Based on this complex network,we can have a more intuitive understanding of the transmission of fluctuation patterns and their fluctuation regular;(2)A new community detection algorithm based on directed weighted network is proposed.The connection relationship between nodes in the network includes direct connection and indirect connection.This algorithm takes the above two connections between nodes into account,adds the distance between nodes in the complex network to the relevant calculation process of intimacy,and proposes the calculation method of intimacy based on the distance between nodes,which can be adjusted adaptively by changing the distance between information granule nodes in the network.Then,according to the degree of intimacy,the community is divided accordingly;(3)On the basis of the division of information granule communities,the Markov chain model is used to further discuss the transfer processes between the fluctuation modes of financial market.Each community is regarded as different state in the Markov chain,and the transfers between communities are regarded as the transfers of states in the Markov chain.By calculating the transfer probability of each state,the most likely target state at the next moment can be obtained.Different states correspond to different fluctuation patterns,which provide a strong basis for the analysis of fluctuation patterns.