Structure and dynamics of financial networks by feature ranking method

Abstract

Much research has been done on time series of financial market in last two decades using linear and non-linear correlation of the returns of stocks. In this paper, we design a method of network reconstruction for the financial market by using the insights from machine learning tool. To do so, we analyze the time series of financial indices of S&P 500 around some financial crises from 1998 to 2012 by using feature ranking approach where we use the returns of stocks in a certain day to predict the feature ranks of the next day. We use two different feature ranking approaches—Random Forest and Gradient Boosting—to rank the importance of each node for predicting the returns of each other node, which produces the feature ranking matrix. To construct threshold network, we assign a threshold which is equal to mean of the feature ranking matrix. The dynamics of network topology in threshold networks constructed by new approach can identify the financial crises covered by the monitored time series. We observe that the most influential companies during global financial crisis were in the sector of energy and financial services while during European debt crisis, the companies are in the communication services. The Shannon entropy is calculated from the feature ranking which is seen to increase over time before market crash. The rise of entropy implies the influences of stocks to each other are becoming equal, can be used as a precursor of market crash. The technique of feature ranking can be an alternative way to infer more accurate network structure for financial market than existing methods, can be used for the development of the market.

Feature ranking and network analysis of global financial indices

“…The average shortest path length is an average of the shortest path lengths between every pair of nodes in the graph. The characteristic path length or the average shortest path length in a cluster can be expressed as [ 3 , 22 ], where d ij is the shortest path length between nodes i and j . The average shortest path length of the threshold network of the global market at threshold θ = 0.047 is shown in Fig 5B .…”

“…The global reaching centrality (GRC) is a global network quantity that shows the flow hierarchy of a complex network, where nodes contribute differently to the dynamics of the network. It is defined for the directed graph as [ 3 , 23 ], where C ( i ) is the local reaching centrality ( LRC ) of node i depicting the proportion of all nodes in the network that can be reached from node i via outgoing links and C max is the maximum value of LRC , V is the set of vertices. The global reaching centrality of the financial threshold network at the mean threshold θ = 0.047 is shown in Fig 5C .…”

“…That’s why global financial market analysis using different concepts and methods grabs the interest of researchers. Reconstructing an unknown network structure from the monitored time series has also been a foremost modern network science problem [ 1 – 3 ]. Many approaches have been used so far to analyze the time series of the global stock market.…”

“…This selection process is based on an impurity function, e.g., Gini Impurity or Information Gain. To find the best split, Gini Impurity estimates Gini feature importance which is the probability of that feature’s contribution in prediction [ 3 ]. A feature is assigned with higher importance if the impurity is reduced significantly by selecting it.…”

“…Feature ranking method is a new approach to the financial system. It was first applied to the time series of US stocks in order to understand market structure over time [ 3 ]. However, still, there was no study on global financial time series using this technique.…”