On interrelations of recurrences and connectivity trends between stock indices

TL;DR

This paper introduces an improved recurrence plot-based estimator, CPR, to analyze connectivity trends between stock indices, revealing erratic market connectivity patterns and emphasizing the importance of significance testing over traditional correlation measures.

Contribution

The paper proposes a modified CPR method that is more robust and sensitive than Pearson's correlation for analyzing dynamic connectivity in financial markets.

Findings

Markets exhibit erratic connectivity, not monotonic increase.

CPR detects high connectivity during the Dot-Com bubble.

CPR is more noise-robust and suitable for short, low-frequency data.

Abstract

Financial data has been extensively studied for correlations using Pearson's cross-correlation coefficient {\rho} as the point of departure. We employ an estimator based on recurrence plots --- the Correlation of Probability of Recurrence (CPR) --- to analyze connections between nine stock indices spread worldwide. We suggest a slight modification of the CPR approach in order to get more robust results. We examine trends in CPR for an approximately 19-month window moved along the time series and compare them to {\rho}. Binning CPR 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 CPR during the Dot-Com bubble by shifting the time series to align their peaks. CPR mainly uncovers that the markets move in and out of periods of strong connectivity erratically, instead of moving monotonously towards increasing global connectivity. This is in contrast to {\rho}, which gives a picture of ever increasing correlation. CPR also exhibits that time shifted markets have high connectivity around the Dot-Com bubble of 2000. We stress on the importance of significance testing in interpreting measures applied to field data. CPR is more robust to significance testing. It has the additional advantages of being robust to noise, and reliable for short time series lengths and low frequency of sampling. Further, it is more sensitive to changes than {\rho} as it captures correlations between the essential dynamics of the underlying systems.