Research On Symbolic Network Conversion Of Stock Time Series Based On STL

It has become an important method to analyze time series by converting them into networks and using the intrinsic topological properties of networks.Stock time series can be abstracted as a financial complex system,which is characterized by numerous factors,complex relationships and difficult to find rules.It is a good research method to convert stock time series into network for analysis.At present,the main problems in converting stock time series into network based on phase space reconstruction,recursion and visibility graph methods are complex conversion process,high algorithm complexity,and too many generated nodes.Based on the symbolic network conversion idea of STL,this paper takes stock closing price as the research object to solve the difficult problem of order determination in the conversion process.Finally,the stock time series is convert-ed into a directed and weighted symbolic network,and the stock time series is analyzed according to the topological attributes of the symbolic network.The differences between this method and the traditional network conversion method of time series are as follows:(1)It is more suitable for network research of stock data.The stock time series is decomposed into seasonal items,trend items and random items,and then the original data are converted into symbols in turn,so as to avoid the problem of a large number of nodes and edges in the network.(2)In the process of series decomposition,the decomposition robustness can be better maintained,and the series with missing data can be decomposed,and the decomposition results will not be distorted by abnormal behavior data.(3)The symbolic network conversion process based on STL method is simple and easy,and does not include double calculation.The main contents of this paper are as follows:1.This paper introduces the stock symbolic network conversion method in detail from three aspects:STL analysis,symbolic processing and network construction,and proposes a symbolic order m_idetermination method.that is,to determine the order of trend item and random item according to the period of seasonal decomposition item.It makes the determination of seasonal order m_s,trend order m_tand random order m_rmore standardized.The Shanghai Composite Index with 6930 data,S&P 500 Index with 8274 data and the Nikkei 225 Index with 7878 data are selected as the experimental data for verification.Finally,compared with the construction methods based on phase space reconstruction,recursion and visibility graph,the results show that the proposed method can simplify the transformation process and reduce the complexity of the algorithm.2.According to the directed and weighted symbolic network based on the Shanghai Composite Index,S&P 500 Index and Nikkei 225 Index:(1)By fitting the degree distribution,it is found that not only the weighted indegree distribution of the three symbolic networks has the characteristics of power-law distribution,but also the weighted outdegree distribution has strong power-law characteristics.At the same time,the closing price data is further analyzed from the topological attributes such as weighting degree,betweenness,pageranks and clustering coef-ficient.The results show that:The greater the weighting degree of a symbolic pattern,the corresponding closing price data is the local maximum or minimum value.The larger the number of betweennness in a certain symbolic pattern,the corresponding closing price data is the inflection point in the whole series.(2)This paper also innovatively carries out modularization processing analysis of symbolic network,and the results show that:The original closing price series corresponding to different modules has its own characteristics.For example,the series corresponding to a specific module is the closing price data when the fi-nancial crisis occurred in 2008.(3)Combined with the average path length and clustering coefficient of the symbolic networks,it is found that the overall volatil-ity of the closing price of S&P 500 Index is the highest,followed by the Nikkei225 index,and the closing price of Shanghai Composite Index is the lowest in the time range from 1990 to 2019.The research of this paper enriches the theory of the traditional definition of the sign network and has certain guiding significance for the property analysis and volatility research of the stock market.