An empirical study on network conversion of stock time series based on STL method

Abstract

A complex network has been widely used to reveal the rule of a complex system. How to convert the stock data into a network is an open issue since the stock data are so large and their random volatility is strong. In this paper, a seasonal trend decomposition procedure based on the loess ([Formula: see text]) method is applied to convert the stock time series into a directed and weighted symbolic network. Three empirical stock datasets, including the closing price of Shanghai Securities Composite Index, S&P 500 Index, and Nikkei 225 Index, are considered. The properties of these stock time series are revealed from the topological characteristics of corresponding symbolic networks. The results show that: (1) both the weighted indegree and outdegree distributions obey the power-law distribution well; (2) fluctuations of stock closing price are revealed by related network topological properties, such as weighting degree, betweenness, pageranks, and clustering coefficient; and (3) stock closing price, in particular, periods such as financial crises, can be identified by modularity class of the symbolic networks. Moreover, the comparison between the [Formula: see text] method and the visibility graph further highlights the advantages of the [Formula: see text] method in terms of the time complexity of the algorithm. Our method offers a new idea to study the network conversion of stock time series.