The structure of financial market is captured using an analysis of non-linear coupling between various stocks using a novel time warping method known as discrete time warping genetic algorithm (dTWGA). In contrast to previous studies which estimate the correlations between different time series, dTWGA can be used to analyse time series with different lengths and with data sampled unevenly. Moreover, since the coupling between different time series or at different periods of time would be changing over time, the time delay for the influence of a time series to reach another time series is generally non-linear and time dependent, which would not be well captured with correlation measurements. Our time warping method provides an alternative to overcome this problem and we apply dTWGA on Dow Jones Index and Hang Seng Index and their constituent stocks. Through dTWGA, the coupling between the stock time series provides a network description of the financial market. We perform different measurements of the resultant financial networks to observe the evolution of their topological structure. We observe consistent major topological changes during market crashes, leading to a significant decrease in the size of the network. We expect these technical analyses provide new insights into the systemic risk of financial market in the perspective of the stability of the corresponding network.

中文翻译：

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通过时间序列的非线性耦合来发展金融网络

通过使用一种称为离散时间规整遗传算法（dTWGA）的新型时间规整方法，对各种股票之间的非线性耦合进行分析，从而掌握了金融市场的结构。与之前的研究估计不同时间序列之间的相关性相比，dTWGA可用于分析具有不同长度和数据采样不均匀的时间序列。此外，由于不同时间序列之间或不同时间周期之间的耦合将随时间而变化，因此，一个时间序列影响到达另一个时间序列的时间延迟通常是非线性的并且与时间相关，这不太好用相关度量捕获。我们的时间规整方法为克服此问题提供了一种替代方法，我们将dTWGA应用于道琼斯指数和恒生指数及其成分股。通过dTWGA，股票时间序列之间的耦合提供了金融市场的网络描述。我们对所得金融网络进行不同的测量，以观察其拓扑结构的演变。在市场崩溃期间，我们观察到一致的主要拓扑变化，从而导致网络规模显着减少。我们希望这些技术分析可以从相应网络的稳定性的角度为金融市场的系统性风险提供新的见解。导致网络规模大大减少。我们希望这些技术分析可以从相应网络的稳定性角度为金融市场的系统性风险提供新的见解。导致网络规模大大减少。我们希望这些技术分析可以从相应网络的稳定性角度为金融市场的系统性风险提供新的见解。