Analysis of financial markets by coupled criticality approach

Analysis of the criticality in finance and economics is an important topic for scholars. The crises are conditions in which unpredictable behavior have been emerged. On the other hand, the contagion from one market to another one due to the complex nature of them is a crucial concept. Therefore, we should consider economies and financial markets as entangled systems that interact with each other, and studying one’s behavior without considering its interacting structures will not provide us with adequate information. In this paper, we have considered the critical states of some emerging and mature markets’ indices. S&P500 and Nikkei 225 as representatives of mature markets, and SSE Composite and TEDPIX as representatives of emerging markets have been analyzed. Coupled criticality emerges when two interacting systems reach their critical state due to their interactions. One of the efficient methods to study the coupled criticality is the bi-variate multifractal random walk model. This method is useful to assess the correlation of rare events and coupled criticality in entangled systems such as financial markets. The observations in this paper show that TEDPIX and S&P500 have higher critical states among others in most time lags by assessing criticality parameter explained in the model, and in longer time lags criticality parameter decreases in all indices. Coupled criticality parameter explained in the model is assessed between each index mentioned and TEDPIX. Results show that TEDPIX and S&P500 have the highest level of coupled criticality. To figure out how long-range time correlation between rare events in each index affect its critical behavior, the data of each index are shuffled, and the criticality parameter is calculated for the shuffled data. From the observations, it can be concluded that this matter has more substantial effect on mature markets. As it is known, shuffling removes the effect of the long-range time correlations. Therefore, the coupled criticality parameter is calculated for the shuffled S&P500 data and TEDPIX. Results show that the long-range correlation of S&P500 data has a significant effect on the coupled criticality behavior of S&P500 and TEDPIX.