On interrelations of recurrences and connectivity trends between stock indices

Financial data has been extensively studied for correlations using Pearson’s cross-correlation coefficient ρ as the point of departure. We employ an estimator based on recurrence plots — the correlation of probability of recurrence ( C P R ) — to analyze connections between nine stock indices spread worldwide. We suggest a slight modification of the C P R approach in order to get more robust results. We examine trends in C P R for an approximately 19-month window moved along the time series and compare them to trends in ρ . Binning C P R into three levels of connectedness (strong, moderate, and weak), we extract the trends in number of connections in each bin over time. We also look at the behavior of C P R during the dot-com bubble by shifting the time series to align their peaks. C P R mainly uncovers that the markets move in and out of periods of strong connectivity erratically, instead of moving monotonically towards increasing global connectivity. This is in contrast to ρ , which gives a picture of ever-increasing correlation. C P R also exhibits that time-shifted markets have high connectivity around the dot-com bubble of 2000. We use significance tests using twin surrogates to interpret all the measures estimated in the study.