EXTREME EVENTS ANALYSIS OF NON-STATIONARY TIME SERIES BY USING HORIZONTAL VISIBILITY GRAPH

In this paper, we analyze the extreme events of non-stationary time series in the framework of horizontal visibility graph (HVG). We give a new definition of extreme events, which incorporates the temporal structure of the series and the degree of the nodes in the HVG. An advantage of the new concept is that it does not require ad hoc treatment even when the non-stationarity arises in time series. We also use the information-theoretic methods to analyze the degree of nodes in the HVG. In the numerical analysis, we study the statistical characterizations of the extreme events of synthetic time series, including the random noises, periodic time series, random walk processes, and the long-range auto-correlated time series. Then, we study 9 time series in stock markets to identify the extreme events evolving in these non-stationary systems. Interestingly, we find that the daily closing price series perform rather close to the random walk processes, while the daily trading volume series behave quite similar to the random noises.