Graph Time Series Analysis Using Transfer Entropy

In this paper, we explore how Schreiber's transfer entropy can be used to develop a new entropic characterisation of graphs derived from time series data. We use the transfer entropy to weight the edges of a graph where the nodes represent time series data and the edges represent the degree of commonality of pairs of time series. The result is a weighted graph which captures the information transfer between nodes over specific time intervals. From the weighted normalised Laplacian we characterise the network at each time interval using the von Neumann entropy computed from the normalised Laplacian spectrum, and study how this entropic characterisation evolves with time, and can be used to capture temporal changes and anomalies in network structure. We apply the method to stock-market data, which represent time series of closing stock prices on the New York stock exchange and NASDAQ markets. This data is augmented with information concerning the industrial or commercial sector to which the stock belong. We use our method not only to analyse overall market behaviour, but also inter-sector and intra-sector trends.