﻿ 对沪深收益指数之间动态条件相关性的实证分析 An Empirical Analysis on the Dynamic Conditional Correlations between the Both Return Indices of Shanghai Stock Exchange and Shenzhen Stock Exchange

Finance
Vol.07 No.03(2017), Article ID:21377,18 pages
10.12677/FIN.2017.73015

An Empirical Analysis on the Dynamic Conditional Correlations between the Both Return Indices of Shanghai Stock Exchange and Shenzhen Stock Exchange

Kejia Yan

Department of Accounting, Finance and Economics, Griffith Business School, Griffith University, Brisbane, Australia

Received: Jun. 29th, 2017; accepted: Jul. 14th, 2017; published: Jul. 17th, 2017

ABSTRACT

Based on the Shanghai Composite Index of Shanghai Stock Exchange and Shenzhen Component Index of Shenzhen Stock Exchange, this paper has calculated the compositional return indices of the both stock markets. The empirical analysis has found that between the both compositional return indices, there are long run and short run cointegration relations, long run and short run bidirectional Granger causality relations, higher dynamic conditional correlation (DCC), higher Clayton lower tail dependence, and higher Gumbel upper tail dependence.

Keywords:Stationary, Cointegration, Causality, Dynamic Correlation, Tail Dependence

Copyright © 2017 by author and Hans Publishers Inc.

1. 引言

2. 数据

(1)

3. 模型

3.1. Jarque-Bera正态性检验

Jarque-Bera正态性检验(Jorion, 2007 [10] ; Alexander, 2008 [11] )是为正态分布而设计的一种统计检验方法。假设表示样本序列的Jarque-Bera统计量，那么，对于大样本，在零假设为正态分布条件下，统计量将收敛于一个自由度为2的卡方分布：

(2)

Table 1. Variable definitions for Shanghai Composite Index, Shenzhen Component Index, return indices, residuals of AR models, dynamic conditional variances and standard residuals of GARCH models

(3)

(4)

(5)

3.2. Ljung-Box自相关性检验

(6)

Ljung & Box (1978) [13] 对统计量进行了修改，而创造出了一个新的统计量，以增加对于有限样本检验的力度。检验时间序列是否为自相关序列，拒绝零假设的条件是，当

(7)

(8)

(9)

(10)

(11)

(12)

(13)

(14)

3.4. 长期协整关系检验

Engle & Granger (1987) [19] 建立了一个两步法协整检验方法，以两个时间序列之间的协整关系为例：第一，建立一个普通最小二乘(OLS)回归模型；第二，检验其误差项序列是否在检验下是平稳序列。由于最小二乘回归运算对于序列的平稳性有影响，所以，Jeffrey (2000) [17] 建议使用一个更高的标准，Davidson & MacKinnon (1993) [20] 门限值标准被推荐用来进行平稳性检验，即在1%、5%、10%概率水平下，统计量的取值不能小于−4.32、−3.78、−3.50的绝对值。

Johansen & Juselius协整检验(Johansen, 1988 [21] ; Johansen & Juselius, 1990 [22] )是另外一种协整检验方法，该检验方法的关键是：当时，通过检验矩阵的秩或者阶数，来检验是否存在。如果矩阵的秩是，即，那么，就存在个协整关系。特征值(eigen value)检验和迹统计(trace static)检验是Johansen & Juselius协整检验的两种方法。其中：

，或 (15)

3.5. 短期协整关系检验

(16)

VECM向量误差修正模型不仅可以揭示两个时间变量之间是否存在短期协整关系，也可以被用来检验两个时间变量之间是否存在短期Granger因果关系。

3.6. 选择优化滞后阶数

，其中 (17)

3.7. Granger因果检验

Granger因果关系(Granger, 1980) [19] 揭示的是：一个时间序列在与时间相关的信息集

3.8. GARCH(1,1)模型

，或, , (18)

, , ,时，GARCH(1,1)模型就可以定义为

, (19)

, (20)

3.9. DCC-GARCH(1,1)模型

, , , (21)

, , , (22)

(23)

(24)

(25)

(26)

(27)

，且 (28)

(29)

3.10. Copula联合分布与尾部依赖关系

Copula函数是用来测定多个变量之间相互依赖关系的一类联合分布函数，由Sklar (1959) [26] 首次提出。假设变量是两个随机变量，它们的边际分布函数由如下概率函数来决定：

(30)

(31)

(32)

Copula密度函数与普通概率密度函数不同，因为Copula密度函数的值总为正，这就说明Copula密度函数在尾部具有较高的取值，有利于表示尾部依赖关系。对于任何随机变量，下尾(lower tail)和上尾(upper tail)依赖系数被定义为：

(33)

(34)

(35)

Clayton Copula的下尾和上尾依赖系数被定义为：

, ,; (36)

(37)

(38)

Gumbel Copula的下尾和上尾依赖系数被定义为：

; (39)

3.11. 参数的最大似然估计

(40)

(41)

(42)

(43)

4. 协整和因果关系检验结果

4.1. 描述性统计值

4.2. 序列自相关性检验

Table 2. Descriptive statistics of the both return indices from Shanghai Composite Index and Shenzhen Component Index

Table 3. Autocorrelation test for Shanghai and Shenzhen stock return indices

4.3. 序列平稳性检验

4.4. Johansen-Juselius协整检验

Johansen-Juselius协整关系检验是考察两个以上非平稳时间序列之间是否可以构成一个平稳线性组合方程的有效工具。两个或者多个非平稳时间序列之间具有Johansen-Juselius协整关系，如果它们之间的线性组合是平稳序列。

Table 4. ADF unit root test under AIC criterion for Shanghai composite index and Shenzhen component index and their return indices

Table 5. Johansen-Juselius cointegration test for the both return indices of Shanghai composite index and Shenzhen component index

4.5. 长期Granger因果关系

4.6. 短期Granger因果关系

Table 6. Long-run linear cointegration models for the both return indices of Shanghai composite index and Shenzhen component index

Table 7. VAR models for the both return indices of Shanghai composite index and Shenzhen component index

Table 8. VECM models for the both return indices of Shanghai composite index and Shenzhen component index

5. DCC动态相关性和Copula函数尾依赖检验结果

5.1. GARCH(1,1) 模型

5.2. DCC模型

Table 9. AR(1) and GARCH(1,1) regressive models for the both return indices of Shanghai composite index and Shenzhen component index

Figure 1. GARCH(1,1) curve of return index from Shanghai Composite Index

Figure 2. GARCH(1,1) curve of return index from Shenzhen Component Index

Table 10. DCC-GARCH(1,1) models from the standard residuals

5.3. Copula尾部依赖关系

Figure 3. Dynamic conditional covariance curve of the standard residuals based on DCC models

Figure 4. Dynamic conditional correlation curve of the standard residuals based on DCC models

Table 11. Parameter estimated values of Gaussian normal distribution and Student-t distribution from the standard residuals

Table 12. Parameter and tail distribution values of Clayton Copula and Gumbel Copula based on Gaussian and Student-t distributions

6. 小结与今后研究

An Empirical Analysis on the Dynamic Conditional Correlations between the Both Return Indices of Shanghai Stock Exchange and Shenzhen Stock Exchange[J]. 金融, 2017, 07(03): 126-143. http://dx.doi.org/10.12677/FIN.2017.73015

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