We consider goodness-of-fit methods for multivariate symmetric and asymmetric stable Paretian random vectors in arbitrary dimension. The methods are based on the empirical characteristic function and are implemented both in the i.i.d. context as well as for innovations in GARCH models. Asymptotic properties of the proposed procedures are discussed, while the finite-sample properties are illustrated by means of an extensive Monte Carlo study. The procedures are also applied to real data from the financial markets.

翻译：我们考虑任意维度下多元对称与非对称稳定帕累托随机向量的拟合优度方法。这些方法基于经验特征函数，既适用于独立同分布情形，也适用于GARCH模型中的创新项。本文讨论了所提程序的渐近性质，并通过广泛的蒙特卡洛研究展示了有限样本性质。此外，这些程序还被应用于金融市场的实际数据。