In this research, we intended to employ the Pearson correlation and a multiscale generalized Shannon-based entropy to trace the transition and type of inherent mutual information as well as correlation structures simultaneously. An optimal value for scale is found to prevent over smoothing, which leads to the removal of useful information. The lowest Singular Value Decomposition Multiscale Generalized Cumulative Residual Entropy (SVDMWGCRE), or SVD Entropy (SVDE), is obtained for periodic–chaotic series, generated by logistic map; hence, the different dynamic, correlation structures, and intrinsic mutual information have been characterized correctly. It is found out that the mutual information between emerging markets entails higher sensitivity, and moreover emerging markets have demonstrated the highest uncertainty among investigated markets. Additionally, the fractional order has synergistic effects on the enhancement of sensitivity with the multiscale feature. According to the logistic map and financial time series results, it can be inferred that the logistic map can be utilized as a financial time series. Further investigations can be performed in other fields through this financial simulation. The temporal evolutions of financial markets are also investigated. Although the results demonstrated higher noisy information for emerging markets, it was illustrated that emerging markets are getting more efficient over time. Additionally, the temporal investigations have demonstrated long-term lag and synchronous phases between developed and emerging markets. We also focused on the COVID-19 pandemic and compared the reactions of developing and emerging markets. It is ascertained that emerging markets have demonstrated higher uncertainty and overreaction to this pandemic.