A cross horizontal visibility graph algorithm to explore associations between two time series

We propose a cross horizontal visibility graph (CHVG) algorithm to explore associations between two time series. As a natural extension of the classic horizontal visibility graph algorithm, the proposed CHVG algorithm can preserve merits of the classic algorithm in construction and implementation. To verify the effectiveness of the CHVG algorithm, we design numerical simulations by generating paired time series with three experimental settings: namely independent autocorrelated series, cross-correlated series with no autocorrelation, and cross-correlated series with autocorrelation. The corresponding CHVGs can be accordingly constructed from these generated pairs of time series. Our results show that the degree distributions of all constructed CHVGs follow exponential distributions P(k) similar to e(-lambda k). Furthermore, the estimated exponent lambda can reflect associations between two time series, mainly due to their cross correlation but also relevant to autocorrelation of individual series. We demonstrate the applicability of the proposed CHVG algorithm by investigating associations between the air pollutant PM10 and the meteorological factors (i.e., temperature and relative humidity) at two stations in Hong Kong. Our algorithm can effectively capture the negative cross correlations between all combinations pairing the pollutant PM10 and one of the two meteorological factors at both stations, which sheds light on understanding, modeling, and prediction of the air pollution process.