Network and Spillovers of Sector Index Returns in China Stock Market

Xue Wang

Southwestern University of Finance and Economics Chengdu�610074�China

Federal Reserve Bank of Atlanta Atlanta, 30309, U.S. Emory University

Atlanta, 30322, U.S. wangxue1207@hotmail.com

Abstract

Using the daily returns data of 18 sector indexes of CSRC industry classification, this paper explores

the spillover effect among the sector indexes returns in China's stock market. We combine the DAG

and SEM methods for the first time to analyze the structure and intensity of the contemporaneous

information spillover effect. Based on the results of the DAG, we improved the Network Analysis

method proposed by Diebold & Yilmaz (2012, 2014) and construct the total and directional spillover

index, to calculate the direction and strength of the overall spillover effect. Moreover, we further

apply the Recursive Variance Decomposition to analyze the time-varying characteristics of

information spillovers. The results show that: the structure and intensity of sector indexes returns

contemporaneous information spillover are consistent with upstream and downstream relationship

of the entity industries. The long-term sector indexes return spillover effect has significant

difference compared with contemporaneous information spillovers, which is mainly affected by the

economic fundamentals. The dynamic spillover index (DSI) have the opposite trend to the Shanghai

Stock Index (SSI). The decline of the dynamic spillover effects is ahead of the rising of the SSI and

when the DSI drops to the lowest point, the SSI reaches its peak point at the same time. In the

prosperous phase of stock market, the sector indexes yield information spillover effects tend to

decline and the impact on the investment risk become weak. While the stock market is in downturn

period, the information spillover effects are remarkably enhanced, which causes the risk conduction

moving more quickly. The research conclusions of this paper have important practical significance

for stock market investors, securities market regulators and macroeconomic policy makers.

Key words: Sector Index Returns; Information Spillover; Investment Portfolio

JEL: G11; G14

1. Introduction The information spillover effect means that the volatility of a market is affected not only by its own pre-volatility but also by the historical volatility of other markets. The transfer of such volatility between markets is called the volatility spillover effect between markets. From the perspective of venture capital and management, the spillover effect of share prices in the industry poses additional risks to investment and management. In order to disperse, resolve and shift the risk of such linkage, it is often necessary to study the spillover effects of stock prices across multiple sectors in order to achieve portfolio composition, risk hedging, and market management. Therefore, examining the spillover effect of stock price volatility in different sectors of the stock market is of great significance for studying the structure, portfolio, risk measurement and management, asset allocation and policy regulation of China's securities market. The spillover effect of the return on the stock market mainly focused on the information spillover and the stock market linkage effect between the stock markets in different countries in the early stage. However, the spillover effect based on the industry level started late. Hassan and Malik (2007) first used the multivariate GARCH-BEKK model to characterize the transfer mechanism of the earnings volatility of the six industry sectors in the United States, indicating that the impact and volatility spillovers among industries are significant. Kallberg & Pasquariello (2008) analyzed the yield data of 82 industrial sectors in the United States and examined the excess returns of industry stocks. Yang Cheng and Yuan Jun (2011) conducted an empirical analysis of the extreme linkage between the industry index returns in China's securities markets and found that the extreme linkage between the industry returns and the market volatility was positively correlated. Liu Qiongfang and Zhang Zongyi (2011) used Copula method to measure the spillover effect between the real estate industry and the financial industry stocks, and found that the two were more tail-related when the market downturn. Hatice et al. (2013) studied the spillover effect of the returns and volatility between the industry indices in the European and American stock markets and found that when considering the trend factors, the volatility of the industry index is similar to the market impact response. The volatility of the industry index Spillover effect better explains the scale of the industry's return. Peri et al. (2017) used the multivariate GARCH model to prove that there is indeed a significant spillover effect between the three industry indices of water, energy and food. However, during the financial crisis in 2008, the spillover effect among the three was weakened. After the crisis Showing a stronger linkage and spillover effect than before the crisis. Using the DCC and ADDC models, Kim & Sun (2017) analyzed the spillover effect between China's 12 industry indices and the S & P 500 index and found that the heterogeneity of different industries' response to external shocks and the linkage between industries occurred over time change.

Most of the studies on the spillover effect of industry index returns can only analyze the overall spillover effect, but cannot measure the direction and intensity of simultaneous information spillover and dynamic information spillover in the market and seldom put the index returns of different industries on the same network Within the study. In this paper, we develop a research method of Directed Acyclic Graph (DAG). Combining this with the structural variance model (SEM), we can not only investigate the structure of information spillover contemporaneous of variables, but also estimate the spillover intensity of synchronization information. Based on this, we calculate the overall information spillover and directional spillover between variables by combining the latest

network analysis (Diebold & Yilmaz, 2012, 2014). At the same time, in order to investigate the time-varying characteristics of information spillover, we use the method of recursive variance decomposition to calculate the dynamic spillover index, including the dynamic overall spillover index and the dynamic directional spillover index. We examine the characteristics of information spillover over time and the impact on the outside world Impact of the reaction. Compared with the previous research, this article based on the transaction data itself, the information spillover effects on the returns of all the different industries in the stock market, including the level of simultaneous, long-term and dynamic information spillover, and the change of spillover index in different periods of stock market. This article examines the information spillover effect in the stock market comprehensively and systematically, and clarifies the direction and intensity of information spillover and the reaction to external shocks.

2. Model and Method

In this paper, a directed acyclic graph (DAG) is combined with a structural equation model (SEM). Using the Directed Acyclic Graph (DAG), we first identify the direction of the spillover of the same period between the index returns of various industries. Based on the analysis results of DAG The SEM model between variables was established, and the EM algorithm was used to derive the information spillover intensity between variables. The combination of DAG and SEM can make each market as a whole system, and identify the causal relationship between them and obtain the transmission path and direction of information flow between markets and the structure and intensity of the same period spillover between markets. We use the method of network analysis based on VAR variance decomposition proposed by Diebold & Yilmaz (2012, 2014) in the analysis of the overall network spillover structure of industry index returns. We apply the analysis results of DAG to the index of spillover It is estimated that the model recognition is based on data-driven completely and solves the sensitivity of traditional variance decomposition to decomposition order. This network analysis method can identify a deeper level of correlation structure and can quantitatively measure the overall intensity and scale of information spillover and judge the direction of information spillover between markets (Diebold & Yilmaz, 2014). This paper further uses the method of recursive variance decomposition to examine the dynamic change trend of information spillover index, and compares it with that of Shanghai Stock Exchange Index to find out the relationship between information spillover rate and dynamic correlation of stock market.

2.1. DAG-SEM method Spirees et al. (2000) constructed a Directed Acyclic Graph (DAG) method as a data-driven method based on the statistical characteristics of the data to effectively identify the concurrent causal structure between variables and to use Graph to indicate the existence and direction of this relationship. The nodes in a directed acyclic graph (DAG) represent random variables, while the edges represent the causal causality between variables. Pearl (1995) proposed the concept of "quarantine set", which can determine the conditional independence between variables in a directed acyclic graph. For any set of variables, where A and B are conditionally independent, there is a "quarantine set" C such that the partial correlation coefficients (conditional correlation coefficients) of A and B are zero. In the DAG analysis, we generally use the PC algorithm proposed by Spirtes et al. (2000) to analyze the (partial) correlation coefficient. For N variables, this algorithm will

continuously analyze from 0 order to N-2 order partial correlation coefficient In order to determine the final causal relationship. In the significance test of the (partial) correlation coefficient, statistics (Spirtes et al., 2000) are usually used to determine whether the (partial) correlation coefficient between variables is zero. The statistics are expressed as follows:

�1�

Where is the sample size, is the number of condition variables, and represents the partial correlation coefficients of variables and when taking variables as condition variables. Let be the partial correlation coefficient of the sample, if the variables , ,all satisfy the normal distribution assumption, then obeys the standard normal distribution.

Most of the existing literatures use DAG only to investigate the contemporaneous spillover structure between variables (Yang Ziyu, 2008; Zhou Yonghong, Deng Weiguang, 2010; Yang & Zhou, 2013), but lack of estimation of spillover strength. Based on the results of DAG analysis, we use the structural equation model (SEM) to analyze the intensity of the spillover effect between variables. The SEM equation is a linear equation. For example, if the analysis result of DAG is "X → Y ← Z", we can establish the corresponding Standard SEM parametric equation:

� �2�

�3�

Among them, are independent random variables subjected to Gaussian distribution. The SEM parameter model defines the probability distribution using graphs and parameters. In these

examples, and as parameters, the values of these parameters in

the SEM parameter model are undetermined and the parameter values are determined by the specific model. According to the causal relationship between the variables obtained by DAG, we establish the SEM model, and in order to obtain the parameters in the SEM model, we further use the maximum expectation (EM) algorithm to estimate the parameters of the model. The EM algorithm is an algorithm that looks for the parameter maximum likelihood or maximum a posteriori estimation in a probabilistic model, which is calculated alternately in two steps: first, the expectation (E) is calculated, the existing estimates of the probabilistic model parameters are used to calculate the hidden variables Then the maximization (M). Using the expectation obtained in the first step, the maximum likelihood of the parametric model is estimated. The estimated parameter values for step M are used in the calculation of the next step E, and the process alternates until the parameter value is estimated. 2.2. Network analysis

Diebold & Yilmaz (2012) proposed a network analysis method to construct the spillover index between variables, including the directional spillover index, the net spillover index and the overall spillover index. The spillover index is based on the variance decomposition feature of vector autoregression (VAR) Measures the direction of information spillover and the size of spillover between variables. This article industry index rate of return spillover construction method is as follows:

'Fisher z

11( ( , | ) ) ( | | 3) ln{[|1 ( , | ) |] [|1 ( , | ) |] }2

Z i j k n n k i j k i j kr r r -= - - ´ + ´ -

n | |k ( , | )i j kr

i j k

( , | )i j kg i j k

( ( , | ) ) ( ( , | ) )Z i j k n Z i j k nr g-

1 2X e e= �Z=

3Y X Za b e= + +

1 2 3e e e� �

1 2 3 1 2e e e e ea b µ µ µ s s� � � � � �3e

s

First consider a VAR (p) model with N industry index returns and a lag order of p:

� �4�

is the N-dimensional column vector, representing N industry spillover index returns, which are all the covariance smoothing process; is the N-dimensional perturbation vector, no sequence related but the components can be related to the same period. , is the covariance matrix. The moving average of the form can be written as , the coefficient matrix obeys the recursive form . The is a N-order unit matrix, when

. The proportion explained by the variable in the variance of the H-period prediction error of

variable is recorded as : �5�

is the covariance matrix of in Eq. (2), is the diagonal element of the covariance matrix. is the selected column vector whose element is 1 while the other are all 0. Under the

structure variance decomposition, we use the row summation to normalize it: .

indicates the spillover effect of industry index rate of return on industry index rate of return . To measure the overall level of market spillover, we construct an overall spillover index

and examine the contribution of information spillover between industry index returns to the overall market volatility.

�6�

At the same time, directional spillover index can be constructed to measure the spillover effect

of index returns from other industries and its external information spillover rate, which reflects the

scale and direction of the overall information spillover of the index returns of individual industries.

�7�

�8�

measures the other variables’ information spillover on the industry index rate of return

, measures the industry index rate of return information on other variables can be

spilled, can be defined as a net spillover index, is a net spillover index

Industry sector index return rate of return on all other sectors of the net spillover effect . The overall

spillover index and the directional spillover index and are based on the results

of the variance decomposition. The spillover index table (Table 1) are available based on the DAG

structural variance decomposition.

Table1 Spillover Indexes Table

... ... ,

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tx

te

. . .(0, )t i i de S! S

0i i i t ix Ae¥= -= S

1 1 2 2i i i p i pA A A A- - -=F +F + +F! 0A 0iA =

0i <

jx

ixHijd

1 2 20 0( ' ) / ( ' ' )H H H

ij ii h i h j h i h h id e A e e A A es -= == S S S S

S e iis

je j

1/H H N Hij ij j ijd d d== S!

Hijd!

j i( )S H

, 1, , 1 , 1,( ) 100 / 100 /N H N H N Hi j i j ij i j ij i j i j ijS H d d d N= ¹ = = ¹= ´S S = ´S

! ! !

1, , 1 1,( ) 100 / 100 /N H N H N Hi j j i ij i j ij j j i ijS H d d d N= ¹ = = ¹= ´S S = ´S

! ! !

"

1, , 1 1,( ) 100 / 100 /N H N H N Hi j j i ji i j ji j j i jiS H d d d N= ¹ = = ¹= ´S S = ´S

! ! !

"

( )iS H!

i ( )iS H! i

( ) ( ) ( )i i iS H S H S H= -! ! i

( )S H ( )iS H! ( )iS H!

1x 2x Nx ( )iS H!

1x 11Hd 12

Hd 1HNd 1 1

N Hj jd=S 1j ¹

... , ... ... ... ... ... ...

... ,

...

�

� ...

� 0

...

3. Empirical Research and Results Analysis 3.1. Data

According to the classification standard of CSRC (2016), listed companies in the domestic securities market are divided into 18 industry categories. The corresponding industry indices include agriculture, forestry, animal husbandry and fishery index, mining index, manufacturing index, hydropower index, construction industry Index, wholesale and retail index, delivery and storage index, accommodation catering index, information technology index, financial index, real estate index, leasing business index, research and technology index, water environment index, health social index, cultural and sports index, education index, comprehensive Enterprise Index and other 18 categories of industry index. The sample interval selected in this paper is the daily closing price of each industry index from January 5, 2007 to May 15, 2017, for a total of 2587 sets of data, the data is from Wind database. The industry index returns use the daily yield from the previous day's closing price to the current closing price, and the closing price on the t and the t-1st, respectively. The calculated profit rates are represented by NLI_R, MII_R, MFI_R, UTI_R, BII_R, WRI_R, TSI_R, ACI_R, ITI_R, FII_R, REI_R, LBI_R, RDI_R, WEI_R, HSI_R, CSI_R, EI_R, and ICI_R, respectively. This article examines the information spillover effects between the returns of 18 industry sectors, including the structure and intensity of information spillover over the same period as well as the direction of medium- and long-term information spillover and the scale of spillover.

Table 2 Descriptive Statistics

Mean Median Maximum Minimum Std. Skewness Kurtosis

ACI_R 0.001 0.002 0.100 -0.100 0.023 -0.551 6.055

BII_R 0.001 0.001 0.144 -0.099 0.022 -0.251 6.906

CSI_R 0.001 0.001 0.100 -0.100 0.025 -0.414 5.297

EI_R 0.001 0.000 0.101 -0.100 0.035 -0.098 4.692

FII_R 0.001 0.000 0.100 -0.099 0.021 0.039 6.251

HSI_R 0.002 0.000 0.409 -0.101 0.032 0.698 14.521

ICI_R 0.001 0.002 0.100 -0.100 0.024 -0.596 5.548

ITI_R 0.001 0.002 0.100 -0.100 0.024 -0.433 5.694

LBI_R 0.001 0.001 0.100 -0.100 0.022 -0.399 5.639

MFI_R 0.001 0.002 0.098 -0.098 0.021 -0.613 6.272

MII_R 0.000 0.000 0.115 -0.100 0.022 -0.184 5.671

NLI_R 0.001 0.002 0.108 -0.100 0.025 -0.392 5.504

RDI_R 0.001 0.001 0.575 -0.100 0.027 3.457 81.441

REI_R 0.001 0.001 0.099 -0.095 0.023 -0.403 5.181

2x 21Hd 22

Hd 2HNd 1 2

N Hj jd=S 2j ¹

Nx 1HNd 2

HNd

HNNd 1

N Hj Njd=S j N¹

( )iS H! 1 1N Hi id=S1i ¹

1 2N Hi id=S2i ¹

1N Hi iNd=Si N¹

, 1N Hi j ijd=Si j¹

( )iS H 1 1 1 1N H N Hi i j jd d= =S - S

1i ¹ 1j ¹1 2 1 2

N H N Hi i j jd d= =S - S

2i ¹ 2j ¹1 1

N H N Hi iN j Njd d= =S - S

i N¹ j N¹( )S H

1 1N Hi id=S 1 2

N Hi id=S 1

N Hi iNd=S , 1,

, 1

N Hi j i j ijN Hi j ij

dd

= ¹

=

S

S

TSI_R 0.000 0.001 0.100 -0.098 0.021 -0.514 6.599

UTI_R 0.001 0.001 0.100 -0.100 0.020 -0.645 7.545

WEI_R 0.001 0.001 0.100 -0.099 0.023 -0.397 5.853

WRI_R 0.001 0.002 0.097 -0.099 0.022 -0.654 6.516

From the descriptive statistical results of the variables, there is no significant difference between

the mean and the volatility of the returns of the various industry indices. The returns of the other indexes except the FII_R, HSI_R and RDI_R are left-deviation distributions. For all the industries, the kurtosis of the index return is significantly greater than 3, showing the typical distribution characteristics of the financial time series of "peak thick tail." Stationarity tests showed that all variables rejected the null hypothesis of unit root at 1% significance level, both of which were stationary time series. 3.2. DAG-SEM analysis of the contemporaneous information spillover structure

We identify the causal structure of variables based on the perturbation correlation coefficient matrix between variables. The analysis results are also important preconditions for further constructing SVAR model, performing structural variance decomposition and measuring spillover index. We use the PC algorithm to analyze the (partial) correlation coefficients between variables by using the perturbation correlation coefficient matrix. The directional edges between the variables that do not have the causation are removed and the causal relationship is judged by the criteria of "quarantine set". The significance level of 5% is used to obtain the information spillover structure of the same period. DAG's analysis shows that a total of 23 yields between the 18 industry index indices indicate the directional edges of contemporaneous causal relationships. Based on the analysis of DAG and further SEM modeling and analysis, we obtain contemporaneous spillover intensity of 18 industry index returns. The results are shown in Figure 1 and Table 3 below.

Figure 1 Industry Index Yield Contemporaneous Information Spillover Network From the structure and intensity of information spillover over the same period, the return on

manufacturing index was most closely linked with other industries during the same period. It was

0.64

0.47

0.59

0.41

0.53 0.74

0.23

0.82

0.74

0.33 0.19 0.81

0.12

0.81 0.51

0.30 0.09

0.72 0.16

0.06

0.49

0.49

HSI_R

ITI_R

MII_R

RDI_R NLI_R

ACI_R

CSI_R

BII_R

LBI_R

MFI_R UTI_R

WRI_R

EI_R ICI_R

TSI_R

WEI_R

FII_R

REI_R 0.30

affected by the information spillover from information technology, research and technology, hydropower, mining, forestry, animal husbandry and fishery over the same period, And will directly affect the water conservancy and environmental industry and wholesale and retail industry over the same period. Although the manufacturing industry receives the most sources of spillover effects, the single industry has a much smaller information spillover rate. The highest is the information technology industry (29.67%), while the lowest is the technology industry, with only 6.27% of it being affected. However, its spillover effect is strong, with spillover effects of 80.87% and 58.6% for the wholesale and retail trade and water conservancy and environmental industries, respectively. Information technology industry contemporaneous the leasing business information strongest spillover effect, up to 80.88%. At the same time, the financial sector index has a strong spillover effect over real estate over the same period, accounting for 82.32% of the total, indicating that the volatility of the financial index will largely affect the real estate index's return over the same period. This is in line with the realities, the real estate industry will attract a lot of money, and changes in financial credit will directly affect the performance of the real estate market. The real estate industry is directly related to the downstream industry is the construction industry, reflected in the stock market, the real estate index yields over the same period the construction industry spill strength of up to 74.14%. Construction industry on its downstream hydropower gas industry over the same period also reached 52.62% spillover. The conduction path of "Finance®Real Estate®Building®Utilities®Manufacture®Wholesale and Retail" reveals the influence of the upstream and downstream of the industry on the same period. The information spillover of industry index rate of return basically agrees with the upstream and downstream industries. Similarly, the spillover effect of agriculture, forestry, animal husbandry and fishery over the same period in the catering industry was 71.94%, while that of the mining industry was 64.29% over the same period of the transportation and warehousing industry, which was in line with the correlation effect among the industries. It is noteworthy that the education sector has no simultaneous linkage with other industry indices over the same period, which is related to its own industry characteristics. The education sector has less impact on the economic environment and has no direct correlation with the industry cycles in other industries. The Composite Index is a composite index with no direct correlation with other sectors over the same period. This shows that manufacturing industry is a traditional industry in our country with very close links with other industries. As a rapidly sprung industry in recent years, information technology and financial industries have shown strong spillover effects on their related industries and upstream and downstream industries. Overall, there is a strong effect of information spillover over the same period in industry index returns, and the industry index has obvious synergies over the same period. Over the same period, the spillover structure and spillover intensity are basically the same as those in the real estate industry. Therefore, it is possible to judge the relevant industry indices and the performance of related industries in the stock market through the operation of the real economy.

Table 3 Industry index yield contemporaneous spillover strength

From To Edge Coef. Std. T P

ACI_R WRI_R 0.0931 0.0092 10.1449 0

BII_R UTI_R 0.5262 0.0132 39.9487 0

FII_R TSI_R 0.2310 0.0149 15.4630 0

FII_R REI_R 0.8232 0.0149 55.3858 0

FII_R MII_R 0.7407 0.0145 51.1632 0

HSI_R ITI_R 0.4929 0.0110 44.7517 0

HSI_R RDI_R 0.4908 0.0137 35.9240 0

ITI_R CSI_R 0.5115 0.0203 25.2562 0

ITI_R MFI_R 0.2967 0.0078 37.8258 0

ITI_R LBI_R 0.8088 0.0088 91.8239 0

LBI_R CSI_R 0.4680 0.0219 21.3638 0

LBI_R WRI_R 0.1155 0.0109 10.6455 0

MFI_R WEI_R 0.5860 0.0170 34.3916 0

MFI_R WRI_R 0.8087 0.0131 61.6540 0

MII_R MFI_R 0.1885 0.0079 23.9560 0

MII_R UTI_R 0.3264 0.0131 24.9613 0

MII_R TSI_R 0.6429 0.0143 44.9451 0

NLI_R ACI_R 0.7194 0.0111 65.0744 0

NLI_R MFI_R 0.1586 0.0069 22.8571 0

RDI_R MFI_R 0.0627 0.0052 12.0914 0

REI_R BII_R 0.7414 0.0110 67.5866 0

REI_R WEI_R 0.4065 0.0152 26.7520 0

UTI_R MFI_R 0.2897 0.0105 27.5632 0

We obtained the same result by choosing regression, EM algorithm, CDS algorithm and

Random Search algorithm, which shows that the result is robust. 3.3. Network analysis of the overall structure of information spillover

3.3.1. Information spillover structure network In this paper, VAR model is constructed by 18 industry index returns, and the optimal lag period is selected according to SC and BIC information criteria as lagged period 1, that is, VAR (1) model, and the structure of VAR model is identified by coincidence spillover structure of DAG The DAG-based SVAR model is derived. , This method of identification does not depend on subjective assumptions or economic theory and is based entirely on the driving of the data itself. It avoids the problems of subjectivity in the past in setting identification matrixes and different economic theory choices resulting in different recognition results and is more objective and reasonable . We then perform structural variance decomposition on the identified SVAR models with a forecast period of 5, thus separating the impact of the industry's own and other variables on the forecast error of index returns for each industry. Then, we calculated the spillover index as follows (Table 4): It can be seen that the manufacturing industry has the highest level of information spillover in other industries, reaching 93.45%, which is consistent with the DAG's coincident spillover result. Indicating that the rate of return is largely affected by the return rate of other industry indexes, and their own interpretation is limited. Secondly, 80.33% of utilities, 79.29% of accommodation and catering industry, were greatly affected by external variables. While the transportation and warehousing industry received the lowest information spillover from other variables, with only 0.95%, it is hardly affected by the index returns of other industries. In addition, index returns of industries such as wholesale and retail trade, education, water conservancy and environment, integrated enterprises

and cultural and sports industries are also not sensitive to the information spillover of other variables and are mainly explained by their own changes. The real estate industry and the financial sector which attracted much attention were also spilled over by other industries, with 67.95% and 42.82% respectively. In terms of the spillover effect of index returns of various industries, the overall spillover effect of wholesale and retail industry on other industries is the strongest, reaching 621.48%, in particular, the information spillover of manufacturing industry has reached 90.35%. Water conservancy and environment industry information industry real estate strong spillover, 49.85%. In addition, the transportation warehousing industry, manufacturing industry and culture and sports industry also have a more obvious effect of foreign information spillover. In contrast, the external information spillover effect of the industry, agriculture, forestry, animal husbandry and fishery on the index returns of other industries is the weakest, only 0.63%. The intensity of external information spillovers in the catering, education, health society, and conglomerate industries is less than 2%, indicating that the return rate of the industry index has no significant impact on other industries. From the perspective of the scale of net information spillover, only the spillover effect of net information in wholesale and retail trade, water conservancy and environmental protection, transportation and warehousing and cultural and sports industries is positive, that is, the spillover of information spillovered by other industries whose scale of external information is larger than the accepted ones. The net information spillover of index returns of other industries is negative, that is, the information spillover of other variables accepted by itself is larger than the scale of information spillover of itself. Among them, the accommodation and catering industry, leasing business, information technology, forestry, animal husbandry and fishery of the net information spillover with -70%, indicating that the rate of return of these types of industry index relative to its own foreign information spillover, more susceptible to other industries The impact of the index rate of return. However, the absolute spillover effect of the returns on education and conglomerates is very small, indicating that the spillover of their external information and the received information spill over can be almost offset by each other. From the net spillover index, we can see that the returns of most industry indices are far more affected by other industries than the intensity of their external information spillover. This shows that in the stock market, most of the industry index returns are affected to a large extent by other industries , The volatility of its return rate is not only explained by its own volatility, but also the influence of the volatility of the return rate of the index of other industries also largely affects its rate of return. The overall spillover index for the entire market is 46.15%, indicating that about 46.15% of the total changes in the industry index returns are the information spillover effects from the index returns of other industries. The linkage and spillover effects of the industry indices undoubtedly explain the industry index return The change is significant.

Compared with the same period of information spillover structure obtained by DAG, there is a significant difference in the information spillover effect of index returns in various industries over the long term. The long-term spillover of external information in the financial, real estate and information technology industries has obviously weakened, indicating that the information spillover rate of the industry index returns has a short duration and is not durable. In the short run, these industries have a strong spillover of external information to other industries. However, in the long run, the industry rate of return is determined mainly by the economic fundamentals and the industry's own stage of development. For emerging industries, information spillover among industries is less sustainable . Manufacturing industry has the strongest information spillover in

other sectors in the long run. As a representative of the real economy and traditional industries, manufacturing industry is inextricably linked with the economic environment. It is closely linked with the return rate of other industry indices both in the short and long term. Information spillover persistence.

Based on the information spillover effect of above industry index returns, we can get different enlightenment from short-term investment and long-term investment. In the short term, the conduction and information spillover of the industry index are similar to those in the physical industry. The investors can judge the linkage between the industries according to the related relations among the entities and industries, and select the stocks of the related industries to achieve the superposition of the scale of returns , But also lead to an increase in risk. The choice of non-related industries or negative correlation between the industry stocks can hedge the risk and reduce portfolio risk. In the long run, the external information spillover effect of emerging industries such as information technology, real estate and financial industries is significantly weaker than that of external information spillovers over the same period, as the industry's return rate is mainly determined by the operation of the economic environment and fundamentals The short-term impact will be weakened. Traditional industries such as manufacturing, shipping and warehousing, cultural and sports industries, and wholesale and retail industries have seen their external information spill over in the long run. This shows that the traditional industries have a sustained impact on the market in the long run, both in the long and short term and in other industries All have strong correlation and information spillover effect. Therefore, in the long-term investors should pay more attention to the operation of the economy to select the investment portfolio, the correlation between industries may be weakened in emerging industries.

Table 4 Information Spillover Structure Network -2 6 22 6 -72 6 2 6 022 6 172 6 2-2 6 282 6 3 2 6 402 6 422 6 532 6 6.2 6 6 2 6 872 6 982 6 2 6 62 6 0A

-2 6

22 6

-72 6

2 6

022 6

172 6

2-2 6

282 6

3 2 6

402 6

422 6

532 6

6.2 6

6 2 6

872 6

982 6

2 6

62 6

8

5 B

8 B

3.3.2. Dynamic information spillover effect analysis The information spillover effect of industry index returns has the characteristics of dynamic

change over time, so investment at different time points also has a greater impact on investment returns, and the reaction of information spillover effects to market information impact is also the focus of our attention. We use the recursive variance decomposition method (Yang & Zhou, 2017) to further examine the dynamic information spillover effects of 18 industry index returns. In contrast to Diebold & Yilmaz (2014) which uses rolling samples to analyze the time-varying features of spillover effects, the information used in the recursive analysis is based on an ever-expanding sample interval rather than a fixed-length time window, resulting in a more robust estimate. In the process of recursive variance decomposition analysis, the paper takes the 1000 trading days from January 5, 2007 to January 4, 2011 as the base period, that is, the first variance analysis of the base period sample data is firstly performed to calculate the industry index And then add one more trading day for analysis of variance and calculation of spillover index. By analogy, a total of 1588 times of variance decomposition analysis and spillover index are calculated to get the dynamic characteristics of spillover index. To examine the robustness of the results, we use the first 500 trading days and 800 trading days recursive variance decomposition, the results are consistent, indicating that the study results are robust.

Figure 3 DSI and SSI changes We compare the measured dynamic overall information spillover index (DSI) with the Shanghai

Securities Index (SSI) and find that the two show almost the opposite trend of change. The overall information spillover index gradually declines from the second half of 2013, The bullish market started in July 2014 (Xu Changsheng and Ma Ke, 2017), but the decline in the industry-wide spillover index shows that the efficiency of information transmission in all sectors is declining and the independence of the industry index's yield volatility is strengthened, which may herald the next bull market. The bull market was officially launched in the first half of 2014. The Shanghai Composite Index rose all the way and reached the highest point of 5166.3 points on June 12, 2015,

1,000

2,000

3,000

4,000

5,000

6,000

.67

.68

.69

.70

.71

.72

2011 2012 2013 2014 2015 2016 2017

SSI DSOI

The highest point 5166.35

The lowest point 67.7%

2013.8.27 2014.7.1 2015.6.12 2016.2.29

The bull market starts

DSOI begins to decline

The stock market becomes stable

DSOI becomes stable

while the dynamic overall information spillover index dropped to a bottom of 67.7% on the same day. The inter-industry index rate of return of the lowest level of information spillover, the stock market so that the impact of soaring industry inter-industry declines, the volatility of the industry index for other industries index volatility of the volatility of response rate weakened, more driven by the broader market rise and the external environment Impact. After the Shanghai Composite Index reached its peak, the broader market began to drop rapidly. From June 12 to July 8, 2015, the Shanghai Composite Index plunged from 5166.35 points to 3507.19 points, a decrease of 32%. During this period, the total market capitalization of A shares has evaporated by 22.77 trillion yuan. As a result, the stock market turmoil and panic intensified. Both retail and institutional investors reduced and sold off. The level of information spillover among industries rebounded rapidly from a low of 67.7% to 71.0% %, Even exceeding the information spillover level before the bull market started. Until the stock market basically recovered its low stability at the end of February 2016, the level of information spillover among industry index returns basically stabilized at the same time and remained at around 70.8%. Through the comparison of the dynamic information spillover index of the industry rate of return and the Shanghai Composite Index, we find that the level of information spillover in the industry index returns almost reverses with the realization of the Shanghai Composite Index. The drop in the rate of return of industry before the rise of the Shanghai Composite Index (about 10 months in advance) and the stronger independence of the industry index may indicate the coming stage of the stock market rising phase in the next stage. With the arrival of the bull market, the dynamic information spillover index is also declining, while the information flow to the lowest level in all sectors, while the Shanghai Composite Index rose to the peak of this round of bull market. After the occurrence of the stock market disaster, the information spillover index also responded promptly. The linkage between industries and the degree of mutual influence rapidly increased. The unfavorable impact of information was promptly transmitted among various industries. Thus, we can see that the industry index rate of return decline in information prior to the rise in the stock market in the stock market to the good and high stage, the industry index volatility greater volatility, active stock market transactions, but the decline in the efficiency of information transfer rate of return The volatility of information cannot be quickly transmitted to other industries. When the stock market weakened and the market downturn, the spillover rate of the industry's profitability rose rapidly, reflecting a higher level of industry index rate of return spillover when the Chinese stock market was adversely affected. For example, in the event of a stock market crash in 2015, the unique phenomenon of "thousands of shares lower limit" frequently appeared in domestic stock markets. The efficiency of information transfer in the stock market is greatly enhanced. The risk transmission in the stock market is significantly enhanced both in information of stocks and in the industry index.

3.3.3. Industry index rate of return of dynamic directional information spillover

Figure 4 Dynamic external dynamic information spillover of every returns

In terms of the changes over time of the external information spillover rate of various industry

index returns, most of the industry index returns are similar to the performance of the overall information spillover index. At the highest bull market in 2015 (June 12, 2015), external information After the spillover level dropped to its lowest point, a stock market disaster started in June 2015, and the Spillover Index rapidly rebounded to or beyond the pre-bull level market. However, there is also a spillover index of industries that varies greatly with the overall spillover index: the intensity of external information spillover of NLMY_R, FII_R and EI_R has been on a downward trend. Even if the bull market rebounds slightly, its external information spillover is also significantly lower than the previous spillover level. In addition, the trend of external information spillover of HSI_R and RDI_R has been in a slowly rising stage before the bull market, and the bull market has a strong stimulating effect on it, prompting a jump in its external information spillover index. By 2016, Six months started in a relatively stable state.

.008

.012

.016

.020

.024

11 12 13 14 15 16 17

NLI_R

.46

.48

.50

.52

.54

11 12 13 14 15 16 17

MII_R

.835

.840

.845

.850

.855

.860

11 12 13 14 15 16 17

MFI_R

.80

.81

.82

.83

.84

.85

.86

11 12 13 14 15 16 17

UT I_R

.76

.77

.78

.79

.80

.81

11 12 13 14 15 16 17

BII_R

.936

.940

.944

.948

.952

11 12 13 14 15 16 17

WRI_R

.85

.86

.87

.88

.89

.90

.91

11 12 13 14 15 16 17

TSI_R

.77

.78

.79

.80

.81

.82

11 12 13 14 15 16 17

ACI_R

.78

.80

.82

.84

.86

11 12 13 14 15 16 17

IT I_R

.58

.60

.62

.64

.66

11 12 13 14 15 16 17

FII_R

.75

.76

.77

.78

.79

11 12 13 14 15 16 17

REI_R

.83

.84

.85

.86

.87

11 12 13 14 15 16 17

LBI_R

.35

.40

.45

.50

.55

.60

11 12 13 14 15 16 17

RDI_R

.79

.80

.81

.82

.83

11 12 13 14 15 16 17

WEI_R

.42

.44

.46

.48

.50

.52

11 12 13 14 15 16 17

HSI_R

.72

.74

.76

.78

.80

.82

11 12 13 14 15 16 17

CSI_R

.83

.84

.85

.86

.87

.88

.89

11 12 13 14 15 16 17

ICI_R

.45

.50

.55

.60

.65

11 12 13 14 15 16 17

EI_R

Figure 5 Dynamic internal dynamic information spillover of every returns

In terms of the information spillover index changes accepted by the index returns of various industries, the performance of different industry indices varies. Most of the industry index returns have received a gradual declining trend from year to year with a gradual decrease in the level of information spillover from other industry indices, with a more moderate decline Such as REI_R, LBI_R, there are "cliff-like" decline, such as RDI_R information spill occurred in the 2015 stock market crash occurred when the jump occurred, and a larger decline, after the flat state. This shows that the rate of information spillover in most sectors after the bull market is over falls. However, the information spillovers accepted by NLI_R, UTI_R, BII_R and ITI_R are generally in an upward trend, indicating that their spillover levels from the outside world have increased significantly after the bull market.

8.2

8.4

8.6

8.8

9.0

9.2

9.4

11 12 13 14 15 16 17

NLI_R

1.35

1.40

1.45

1.50

1.55

1.60

11 12 13 14 15 16 17

MII_R

1.500

1.525

1.550

1.575

1.600

1.625

1.650

11 12 13 14 15 16 17

MFI_R

.04

.05

.06

.07

.08

.09

.10

11 12 13 14 15 16 17

UT I_R

.045

.050

.055

.060

.065

.070

11 12 13 14 15 16 17

BII_R

.060

.065

.070

.075

.080

.085

.090

11 12 13 14 15 16 17

WRI_R

.02

.03

.04

.05

.06

.07

11 12 13 14 15 16 17

TSI_R

.02

.03

.04

.05

.06

.07

11 12 13 14 15 16 17

ACI_R

.02

.04

.06

.08

.10

11 12 13 14 15 16 17

IT I_R

.05

.06

.07

.08

.09

.10

11 12 13 14 15 16 17

FII_R

.06

.07

.08

.09

.10

.11

11 12 13 14 15 16 17

REI_R

.015

.020

.025

.030

.035

.040

.045

11 12 13 14 15 16 17

LBI_R

.012

.014

.016

.018

.020

.022

11 12 13 14 15 16 17

RDI_R

.005

.010

.015

.020

.025

11 12 13 14 15 16 17

WEI_R

.008

.010

.012

.014

.016

11 12 13 14 15 16 17

HSI_R

.000

.004

.008

.012

.016

11 12 13 14 15 16 17

CSI_R

.008

.012

.016

.020

.024

.028

.032

11 12 13 14 15 16 17

ICI_R

.000

.005

.010

.015

.020

.025

11 12 13 14 15 16 17

EI_R

Figure 6 Dynamic net dynamic information spillover of every returns

Judging from the changes in the net excess index of the index returns of various industries, the net spillover index of NLI_R, MII_R and MFI_R is negative while the net spillover of other industry index returns is positive in the sample interval, indicating that most of the industry index returns More foreign information spillover than the accepted information spillover. And only FII_R, EI_R net information spillover index has been showing a downward trend, and other net information spillover positive for the industry index rate of return in the bull market in 2015 when the sudden jump, showing a strong net foreign information spillover effect. Relative to the net spillover effect before the bull market, the net information spillover of most industry index returns has been significantly increased.

The dynamic directional spillover index of the industry index returns shows that the information spillovers of various industry indexes vary widely and the reactions to external shocks are also quite different. However, on the whole, the impact of the stock market bull market can increase the rate of return of industry index to external information spillover Level, while the received level of information spillover has a weakened effect. The net spillover effect of most industry index returns is positive, and the negative impact of the outside world will increase the level of net information spillover. Therefore, when the stock market is in a good or rising stage, the overall information spillover rate of the industry rate of return will decrease accordingly. Therefore, in the upward phase of the stock market, the linkage between industry indices and the information spillover effect will be weakened, and investors may Reduce investment in the portfolio of information spillover considerations. In the downward phase of the stock market, the level of information spillover among industry indices is significantly higher. To diversify and transfer risks, stock investors should pay more attention to the information spillover effects among industries because information spillover effects among industries are stronger and different industry indices

-9.4

-9.2

-9.0

-8.8

-8.6

-8.4

-8.2

11 12 13 14 15 16 17

NLI_R

-1.10

-1.05

-1.00

-0.95

-0.90

-0.85

11 12 13 14 15 16 17

MII_R

-.84

-.80

-.76

-.72

-.68

-.64

11 12 13 14 15 16 17

MFI_R

.70

.72

.74

.76

.78

.80

.82

11 12 13 14 15 16 17

UT I_R

.68

.70

.72

.74

.76

11 12 13 14 15 16 17

BII_R

.85

.86

.87

.88

.89

11 12 13 14 15 16 17

WRI_R

.81

.82

.83

.84

.85

.86

11 12 13 14 15 16 17

TSI_R

.740

.745

.750

.755

.760

.765

.770

11 12 13 14 15 16 17

ACI_R

.68

.72

.76

.80

.84

11 12 13 14 15 16 17

IT I_R

.50

.52

.54

.56

.58

11 12 13 14 15 16 17

FII_R

.66

.67

.68

.69

.70

.71

.72

11 12 13 14 15 16 17

REI_R

.80

.81

.82

.83

.84

.85

11 12 13 14 15 16 17

LBI_R

.36

.40

.44

.48

.52

.56

11 12 13 14 15 16 17

RDI_R

.78

.79

.80

.81

.82

.83

11 12 13 14 15 16 17

WEI_R

.42

.44

.46

.48

.50

11 12 13 14 15 16 17

HSI_R

.72

.74

.76

.78

.80

11 12 13 14 15 16 17

CSI_R

.81

.82

.83

.84

.85

.86

11 12 13 14 15 16 17

ICI_R

.45

.50

.55

.60

11 12 13 14 15 16 17

EI_R

the spread of risk between the more rapid, and some industries between the spillover of information is persistent, which requires investors to carefully choose to invest in the underlying industry stocks, portfolio hedge the risk of investment.

4. Conclusions

By analyzing the structure and intensity of the same period information spillover of 18 industry

index returns, the overall level of information spillover and directional information spillover, as well as the overall dynamic spillover and the directional dynamic spillover of various industries, this paper systematically and comprehensively examines the index returns of different industries in the stock market Rate of information spillover effect. The result shows that the spillover structure and spillover intensity of the index over the same period are basically consistent with those of the real industry through the spillover structure and spillover intensity of the industry index. Through the operation of the real economy, the relevant industry indices and the performance of related industries in the stock market can be judged. In the long run, the information spillover effect of index returns in various industries is significantly different. The spillover effect of traditional industries in manufacturing industry may be persistent. However, the information spillover effects in emerging industries such as financial industry and information technology industry are mainly affected by the economic fundamentals Impact. Based on the direction and intensity of information spillover, investors can deduce the changes of index returns in other industries, diversify their investment portfolios and hedge strategies among industries, thus effectively reducing market risks and increasing portfolio investment returns. The dynamic spillover effect of the industry index returns shows that the favorable market impact can increase the level of overall information spillover and the level of external information spillover of various industry indices, and has a weaker effect on the level of information spillover accepted. The stock market to the good stage, industry index returns spillover effect between the decline, the impact of information spillover on investment risk weakened. In the downward phase of the stock market, the information spillover effect is significantly enhanced, and the transmission and transfer of risks are accelerated. This shows that investors should pay more attention to the information spillover effect between industry indices in the stock market weakening period. Based on the characteristics of different industries, Portfolio investment, in order to achieve the risk of dispersion and avoidance. From the perspective of securities market regulation, it is also of great significance to master the information spillover effect among industries in terms of stabilizing the market and strengthening supervision. Policy information shocks can lead to changes in the information spillover effect between index returns in some industries and the shocks can quickly spread and be transmitted to other industries. This information spillover may persist, adversely affecting the stability of the stock market. Grasping the mode of transmission of information between industries can effectively prevent the financial risks caused by the fluctuation of the stock price index in the stock market. Regulators should focus on the characteristics of information transmission among industries and their response to the impact of external information to develop regulatory measures, focusing on strengthening the supervision of industries with strong external information spillover effects and further optimize the allocation of market resources and financial risk hedges, So as to realize the steady and healthy development of the market.

From the perspective of the makers of macroeconomic policy, the steady operation of the real economy is the basis for the sound development of the securities market. The information spillover among industries fundamentally comes from the connection and influence among the industries in the real economy. This requires that macroeconomic In terms of policy formulation, it is necessary to consider the interaction among industries and promote the industrial transformation and upgrading and structural rationalization, so as to exert a positive regulatory role on the real economy and the fictitious economy and further promote the healthy and long-term development of the national economy.

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