THESIS
2020
viii, 44 pages : illustrations ; 30 cm
Abstract
In this thesis, we study the stock dependence based on co-jumps. We construct
two separated co-jumps networks according to whether the market jumps or not and use
the Spectral Clustering On Ratios-of-Eigenvectors (SCORE) algorithm proposed by Jin
et al. [2015] for clustering or community detection. We find the two networks have significantly
different clustering results. On the one hand, when the market does not jump, our
clustering result can almost perfectly recover some Global Industry Classification Standard
(GICS) sectors; on the other hand, it merges the GICS sectors into a community.
However, when the market jumps, many stocks co-jump with the market. The clustering
result shows relationships from upstream to downstream in a supply chain.
Mathematically, we extend the SC...[
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In this thesis, we study the stock dependence based on co-jumps. We construct
two separated co-jumps networks according to whether the market jumps or not and use
the Spectral Clustering On Ratios-of-Eigenvectors (SCORE) algorithm proposed by Jin
et al. [2015] for clustering or community detection. We find the two networks have significantly
different clustering results. On the one hand, when the market does not jump, our
clustering result can almost perfectly recover some Global Industry Classification Standard
(GICS) sectors; on the other hand, it merges the GICS sectors into a community.
However, when the market jumps, many stocks co-jump with the market. The clustering
result shows relationships from upstream to downstream in a supply chain.
Mathematically, we extend the SCORE from the adjacency matrix to the Poisson
matrix (SCORE-P) and prove that SCORE-P enjoys strongly consistent property under
some mild assumptions. It benefits from the development of random matrix theory, where
the sub-exponential case Bernstein inequality is constructive Tropp [2012].
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