Global recurrence quantification analysis and its application in financial time series

This study proposes a modified recurrence quantification analysis, called global recurrence quantification analysis (GRQA). It is well known that the recurrence threshold is an important parameter in traditional recurrence quantification analysis. However, in existing researches, the selection of recurrence thresholds is often based on 'rules of thumb.' As many studies have shown, recurrence analysis and its quantifiers are strongly dependent on the evaluation of the vicinity threshold parameter, which indicates that a selected threshold may have an adverse effect on exploring signal inherent information and the interrelationship between different sequences. Therefore, GRQA is initialized in this paper to measure the vertical and diagonal structures of recurrence plots in a more objective way, because it considers all the information carried by all potential values of the threshold. The information described by GRQA is determined by the sequence itself and is not affected by specific thresholds. GQRA can also clearly depict the dynamical similar characteristics and recursive trajectories between sequences, which have not appeared in previous researches. We apply this method to the financial time series to find some useful information. It reveals that SZSE and SSE show similar inherent dynamic characteristics via GQRA statistics curves, and DJI and NASDAQ are similar to each other as well, while HSI is like a combination of these two groups with both of their characteristics, which is consistent with its financial background.