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Nonparametric estimation of general multivariate tail dependence and applications to financial time series

机译:一般多元尾部依赖的非参数估计及其在金融时间序列中的应用

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In order to analyse the entire tail dependence structure among random variables in a multidimensional setting, we present and study several nonparametric estimators of general tail dependence functions. These estimators measure tail dependence in different orthants, complementing the commonly studied positive (lower and upper) tail dependence. This approach is in line with the parametric analysis of general tail dependence. Under this unifying approach the different dependencies are analysed using the associated copulas. We generalise estimators of the lower and upper tail dependence coefficient to the general multivariate tail dependence function and study their statistical properties. Tail dependence measures come as a response to the incapability of the correlation coefficient as an extreme dependence measure. We run a Monte Carlo simulation study to assess the performance of the nonparametric estimators. We also employ selected estimators in two empirical applications to detect and measure the general multivariate non-positive tail dependence in financial data, which popular parametric copula models commonly applied in the financial literature fail to capture.
机译:为了分析多维设置中随机变量之间的整个尾部依赖结构,我们提出并研究了一般尾部依赖函数的几种非参数估计量。这些估算器可测量不同矫正器中的尾部依存关系,从而补充了通常研究的正(下部和上部)尾部依存关系。该方法与一般尾巴相关性的参数分析一致。在这种统一方法下,使用相关联的关联词分析了不同的依赖性。我们将下尾依赖系数和上尾依赖系数的估计值推广到一般的多元尾依赖函数,并研究它们的统计特性。尾部依赖度量是对相关系数的无能作为极端依赖度量的回应。我们进行了蒙特卡洛模拟研究,以评估非参数估计器的性能。我们还在两个经验应用中采用了选定的估计量,以检测和测量金融数据中一般的多元非正尾相关性,而在金融文献中通常无法使用流行的参数关联模型。

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