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...[ Read more ]

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.