Memon Bilal Ahmed, Yao Hongxing
School of Finance and Economics, Jiangsu University, Zhenjiang 212013, China.
Entropy (Basel). 2019 Mar 5;21(3):248. doi: 10.3390/e21030248.
We studied the cross-correlations in the daily closing prices of 181 stocks listed on the Pakistan stock exchange (PSX) covering a time period of 2007-2017 to compute the threshold networks and minimum spanning trees. In addition to the full sample analysis, our study uses three subsamples to examine the structural change and topological evolution before, during, and after the global financial crisis of 2008. We also apply Shannon entropy on the overall sample to measure the volatility of individual stocks. Our results find substantial clustering and a crisis-like less stable overall market structure, given the external and internal events of terrorism, political, financial, and economic crisis for Pakistan. The subsample results further reveal hierarchal scale-free structures and a reconfigured metastable market structure during a postcrisis period. In addition, time varying topological measures confirm the evidence of the presence of several star-like structures, the shrinkage of tree length due to crisis-related shocks, and an expansion in the recovery phase. Finally, changes of the central node of minimum spanning trees (MSTs), the volatile stock recognition using Shannon entropy, and the topology of threshold networks will help local and international investors of Pakistan Stock Exchange limited (PSX) to manage their portfolios or regulators to monitor the important nodes to achieve stability and to predict an upcoming crisis.
我们研究了在2007年至2017年期间在巴基斯坦证券交易所（PSX）上市的181只股票的每日收盘价的互相关性，以计算阈值网络和最小生成树。除了全样本分析之外，我们的研究还使用了三个子样本，来检验2008年全球金融危机之前、期间和之后的结构变化和拓扑演变。我们还对整个样本应用香农熵来衡量个股的波动性。鉴于巴基斯坦的恐怖主义、政治、金融和经济危机等外部和内部事件，我们的结果发现了大量的聚类以及类似危机的总体市场结构不稳定。子样本结果进一步揭示了危机后时期的分层无标度结构和重新配置的亚稳市场结构。此外，时变拓扑度量证实了存在几个星状结构、与危机相关的冲击导致树长收缩以及复苏阶段扩张的证据。最后，最小生成树（MST）中心节点的变化、使用香农熵识别波动股票以及阈值网络的拓扑结构，将有助于巴基斯坦证券交易所有限公司（PSX）的本地和国际投资者管理其投资组合，或帮助监管机构监测重要节点以实现稳定并预测即将到来的危机。
