Could network analysis of horizontal visibility graphs be faithfully used to infer long-term memory properties in real-world time series?

Abstract

Mapping time series to complex networks has great potential to investigate their temporal structures. Some previous studies have been carried on time series generated from idealized stochastic models and found that there are inherent associations between long-term memory (LTM) of pure long-range correlated time series and topological parameters (TPs) of their networks, which is thought as a new prospective to extract information from time series. However, output time series from natural systems seldom take so idealized structures as those from idealized stochastic models, and there is usually some unconsidered information inherited in them, which makes these derived associations questionable. To check and generalize these conclusions acquired from idealized stochastic models, horizontal visibility graph (HVG) algorithm is employed to map time series to their horizontal visibility networks. Firstly synthetic time series with known mixed correlations (apart from LTM) have been analyzed and results indicate that topological parameters (TPs) of HVG networks are not solely dominated by the strength of LTM, other factors such as white noise, short-term correlation (STC) and nonlinear correlations are also playing crucial roles. Taking this fact into account, after some preprocessing treatments have been carried out, the LTM of daily mean air temperature series can indeed be inferred by means of the inherent associations between LTM of pure long-range correlated time series and TPs of their networks.