Nighttime lights (NTLs) have been used as a proxy for economic growth in recent years. To verify the effectiveness of NTL in measuring regional economies, this article studies the regional economic convergence phenomenon in China’s provinces by a comparative analysis of NTL data and GDP data from 1992 to 2013. It is found that there is a significant difference between the results of club convergence between NTL and GDP; GDP high-growth clubs are mainly concentrated in the east and central areas, while NTL’s high-growth clubs are mostly concentrated in the central and west areas. Besides, the growth rate gaps between GDP clubs are relatively flat, while the growth rate gaps between NTL clubs are large. From the perspective of influencing, factors of the regional convergence, technological innovation, and industrial structure have a significant impact on GDP and NTL, and industrial structure has opposite effects on GDP clubs and NTL clubs. Besides the above factors, for NTL convergence clubs, population growth rate, economic openness, and resource consumption are also significant.

In recent years, persistent homology (PH) and topological data analysis (TDA) have gained increasing attention in the fields of shape recognition, image analysis, data analysis, machine learning, computer vision, computational biology, brain functional networks, financial networks, haze detection, etc. In this article, we will focus on stock markets and demonstrate how TDA can be useful in this regard. We first explain signatures that can be detected using TDA, for three toy models of topological changes. We then showed how to go beyond network concepts like nodes (0-simplex) and links (1-simplex), and the standard minimal spanning tree or planar maximally filtered graph picture of the cross correlations in stock markets, to work with faces (2-simplex) or any k-dim simplex in TDA. By scanning through a full range of correlation thresholds in a procedure called filtration, we were able to examine robust topological features (i.e. less susceptible to random noise) in higher dimensions. To demonstrate the advantages of TDA, we collected time-series data from the Straits Times Index and Taiwan Capitalization Weighted Stock Index (TAIEX), and then computed barcodes, persistence diagrams, persistent entropy, the bottleneck distance, Betti numbers, and Euler characteristic. We found that during the periods of market crashes, the homology groups become less persistent as we vary the characteristic correlation. For both markets, we found consistent signatures associated with market crashes in the Betti numbers, Euler characteristics, and persistent entropy, in agreement with our theoretical expectations.