There are many research papers yielding the financial data models, where returns are tied either to the fundamental analysis or to the individual, often irrational, behaviour of investors. In the second case the bubble followed by the crisis is possible on the market. Such bubble or crisis is reflected by the cross-correlated extreme positive or negative returns of many assets. Such returns are modelled by the copula with the meaningful tail dependencies. The typical model of such cross-correlation provides the t-Student copula. The author demonstrates that the mutual information tied to this copula can be measured by the 4th order multivariate cumulants. Tested on the artificial data, the 4th order multivariate cumulant approach was used successfully for the financial crisis detection. For this end the author introduces the outliers detection algorithm. In addition this algorithm displays the potential application for the crisis prediction, complementary to the auto-correlation analysis.

有许多研究论文产生了财务数据模型，其中收益与基本分析或投资者个人（通常是非理性的）行为相关。在第二种情况下，市场上可能会出现泡沫和危机。这种泡沫或危机反映在许多资产之间相互关联的极端正或负收益上。这样的回报是由copula用有意义的尾部依赖性建模的。这种互相关的典型模型提供了t型学生语系。作者证明，与该系动词相关的相互信息可以通过四阶多元累积量来度量。经过人工数据测试，四阶多元累积量方法已成功用于金融危机检测。为此，作者介绍了异常值检测算法。此外，该算法还显示了潜在的危机预测应用，可对自相关分析进行补充。