THESIS
2023
1 online resource (xii, 88 pages) : illustrations (some color)
Abstract
In this thesis, we use pairwise co-jump networks to study stock dependence among
a large number of stocks. In Chapter 2, we propose a Degree-Corrected Block Model
with Dependent Multivariate Poisson edges (DCBM-DMP). To estimate the community
structure, we extend the SCORE algorithm in Jin [2015] and develop a Spectral
Clustering On Ratios-of-Eigenvectors for networks with Dependent Multivariate Poisson
edges (SCORE-DMP) algorithm. We prove that SCORE-DMP enjoys strong consistency
in community detection. Empirically, using high-frequency data of S&P 500 constituents,
we construct two co-jump networks according to whether the market jumps and find that
they exhibit different community features than GICS.
In Chapter 3, we extend our model to involve the mixed membership structure.
We deve...[
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In this thesis, we use pairwise co-jump networks to study stock dependence among
a large number of stocks. In Chapter 2, we propose a Degree-Corrected Block Model
with Dependent Multivariate Poisson edges (DCBM-DMP). To estimate the community
structure, we extend the SCORE algorithm in Jin [2015] and develop a Spectral
Clustering On Ratios-of-Eigenvectors for networks with Dependent Multivariate Poisson
edges (SCORE-DMP) algorithm. We prove that SCORE-DMP enjoys strong consistency
in community detection. Empirically, using high-frequency data of S&P 500 constituents,
we construct two co-jump networks according to whether the market jumps and find that
they exhibit different community features than GICS.
In Chapter 3, we extend our model to involve the mixed membership structure.
We develop a Mixed Spectral Clustering On Ratios-of-Eigenvectors for networks with
Dependent Multivariate Poisson edges (Mixed-SCORE-DMP) algorithm. We show that
Mixed-SCORE-DMP is asymptotically consistent in estimating the mixed membership
structures. We also address the important question of estimating the unknown number of
communities. The advantage of our method is that it is a unified approach for different network models with different sparsity levels. Empirically, we find that the purity of
individual stocks has a strictly monotonic relationship with both volatility and the Sharpe
ratio, and the peer momentum defined by the mixed membership has a stronger reversal
effect. We further show that the mixed structure of co-jump networks helps better than
pure community detection in stock return prediction.
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