This paper introduces an innovative method for constructing copula models capable of describing arbitrary non-monotone dependence structures. The proposed method enables the creation of such copulas in parametric form, thus allowing the resulting models to adapt to diverse and intricate real-world data patterns. We apply this novel methodology to analyze the relationship between returns and trading volumes in financial markets, a domain where the existence of non-monotone dependencies is well-documented in the existing literature. Our approach exhibits superior adaptability compared to other models which have previously been proposed in the literature, enabling a deeper understanding of the dependence structure among the considered variables.

翻译：本文介绍了一种构建能够描述任意非单调依赖结构的copula模型的创新方法。所提出的方法允许以参数形式创建此类copula，从而使生成的模型能够适应多样且复杂的真实世界数据模式。我们将这一新颖方法应用于分析金融市场中收益率与交易量之间的关系——该领域已有文献充分证明了非单调依赖性的存在。与文献中先前提出的其他模型相比，我们的方法表现出更强的适应性，能够更深入地理解所考察变量间的依赖结构。