Nature of stock index interrelations

Abstract

The main goal of this study is to present an application of recurrence-based techniques in analyzing certain aspects of interrelations among stock indices of the world. In the past, financial data has been extensively studied for correlations using Pearson's cross-correlation coefficient Rho. In the current study, an estimator based on recurrence plots - the Correlation of Probability of Recurrence (CPR) - is used to analyze connections between nine stock indices spread worldwide. A slight modification of the CPR is suggested here in order to get more robust results.

Temporal trends in the CPR are examined by moving an approximately 19-month window along the time series and the results obtained are then compared to those obtained by carrying out a similar analysis with Rho. Binning CPR into three levels of connectedness: strong, moderate and weak, temporal trends in the number of connections in each of these three bins are extracted. Furthermore, the behavior of CPR during the Dot-Com bubble is observed by shifting the time series to align their peaks. This was done to observe the manner in which different stock markets behave during financial crisis.

This analysis, using the extended CPR approach, reveals 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, indicating that markets have similar dynamical nature during a crisis irrespective of the actual date when they crash.

The importance of significance testing in interpreting measures applied to field data is highlighted in this work, especially the use of Twin Surrogates as a reliable method to generate surrogate data sets required for significance testing. CPR proves to be more robust to significance testing than Rho. It also has the additional advantages of being robust to noise, as well as being reliable for short time series lengths and low and irregular frequency of sampling. Further, it is more sensitive to changes than Rho as it captures correlations between the essential dynamics of the underlying systems.

The work done in this project forms the subject of the following paper.

On interrelations of recurrences and connectivity trends between stock indices, B. Goswami, G. Ambika, N. Marwan, J. Kurths, arXiv:1103.5189v1,- submitted to Physica A, 2011.