我們發展一個建立金融網絡的兩階段程序。在第一階段中，我們為金融資產報酬率建立向量自
我迴歸（VAR）模型。為了克服高維模型中的選擇變量問題，我們採用三種方法：去除偏誤
的Lasso; 適應的Lasso; 逐步迴歸法。我們使用VAR 模型的係數來構建網絡的鄰接矩陣，這決
定了網絡中節點之間的連通性和關係。在第二階段中，我們將每個節點的連接節點視為解釋
變量，構建網絡向量自我迴歸（NAR）模型。此NAR模型用以探討金融系統的網絡和動量效
應，並且進行干擾分析。

We develop a two-stage procedure for constructing financial network. In the first stage,
we build vector autoregressive (VAR) models for financial asset returns. To overcome
the variable selection problem in high-dimensional models, we adopt the three methods:
debiased Lasso, adaptive Lasso and a stepwise regression method. We use the coefficients
of the VAR models to construct the adjacency matrix of the network, which determines the
connectedness and the relationships among the nodes within the network. In the second
stage, we treat each node’s connected nodes as an explanatory variable and build a network
vector autoregressive (NAR) model. This NAR model is then utilized to investigate the
network and momentum effects of the financial system and perform intervention analysis.

誌謝 i
摘要 ii

Abstract iii

1 Introduction 1

2 Granger causality network model 3

2.1 Debiased Lasso VAR estimation . . . . . . . . . . . . . . . . . . . . . . . . 3

2.2 Adaptive Lasso VAR estimation . . . . . . . . . . . . . . . . . . . . . . . . 7

2.3 OGA+HDIC+Trim VAR estimation . . . . . . . . . . . . . . . . . . . . . 7

3 Network vector autoregression 9

3.1 NAR model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3.2 Intervention analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

4 Further study on the two stage network 11

4.1 Estimation comparison for the VAR model . . . . . . . . . . . . . . . . . . 11

4.2 Relationship between VAR and NAR coefficients . . . . . . . . . . . . . . . 12

4.3 Intervention analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

5 Empirical study 14

6 Conclusion 19

7 Future work 20

7.1 Penalized quantile regression estimation with Lasso . . . . . . . . . . . . . 20

7.2 Quantile NAR model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

7.3 Simulation study for quantile regression . . . . . . . . . . . . . . . . . . . . 22

7.3.1 Estimate network via VAR and quantile regression models . . . . . 22

7.3.2 Fit quantile NAR model . . . . . . . . . . . . . . . . . . . . . . . . 24

7.3.3 Debiased Lasso VAR and Lasso VAR + LSE . . . . . . . . . . . . . 26

7.4 Empirical study for quantile regression . . . . . . . . . . . . . . . . . . . . 27

8 References 30

9 Appendix 32

9.1 Appendix A: Company Tables . . . . . . . . . . . . . . . . . . . . . . . . . 32

9.2 Appendix B: Choice of the quantile regression Lasso penalty parameter λi 34

9.3 Appendix C: Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

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