Abstract
In this paper we focus our attention on multi-dimensional copula models of returns of the indexes of selected prominent international financial markets. Our modeling results, based on elliptic copulas, 7-dimensional vine copulas and hierarchical Archimedean copulas demonstrate a dominant role of the SPX index among the considered major stock indexes (mainly at the first tree of the optimal vine copulas). Some interesting weaker conditional dependencies can be detected at it’s highest trees. Interestingly, while global optimal model (for the whole period of 277 months) belong to the Student class, the optimal local models can be found (with very minor differences in the values of GoF test statistic) in the classes of vine and hierarchical Archimedean copulas. The dominance of these models is most striking over the interval of the financial market crisis, where the quality of the best Student class model was providing a substantially poorer fit.
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Notes
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Another, a rather exotic result is given by [25] who showed conditions under which the so-called Kautz graph (such a line graph of a complete digraph that has diameter 2) is a Cayley graph (an important class because of symmetry and easiness of their generation).
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The support of the grants APVV-14-0013 and VEGA 1/0420/15 is kindly announced.
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Bacigál, T., Komorníková, M., Komorník, J. (2020). Multidimensional Copula Models of Dependencies Between Selected International Financial Market Indexes. In: Kulczycki, P., Kacprzyk, J., Kóczy, L., Mesiar, R., Wisniewski, R. (eds) Information Technology, Systems Research, and Computational Physics. ITSRCP 2018. Advances in Intelligent Systems and Computing, vol 945. Springer, Cham. https://doi.org/10.1007/978-3-030-18058-4_28
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