Empirical Analysis of the “China‒US factor” in Stock Market Linkages

ABSTRACT

This article studies the economic impact of China and the U.S. from 2011 to 2023 through stock market linkages. A bivariate VAR model is used for nonlinear Granger causality analysis. The results show that the U.S. economy’s dominance remains unshaken, impacting the world economy. Despite China’s progress and significant role in the global economy, it cannot yet impact the U.S. economy. Understanding this is crucial for global economic patterns, the political state, and enriching global economic stability and development.

KEYWORDS:

• Stock market
• volatility index
• comovement
• nonlinear Granger causality

JEL:

• F30, G15, F44

1. Introduction

As the world’s largest economies, China and the United States have always played important roles in the global economy. In recent years, the global economy has become increasingly integrated, the degree of liberalization of financial markets has continued to increase, the connections of capital markets in different countries have become more closely linked, and the correlation characteristics between stock markets have become more prominent (Stiglitz 2004). In the context of global financial integration, effectively improving the efficiency of capital flow allocation and the operation of stock markets can promote the effective and stable development of the international economy to a certain extent. For a country (region), the stock market can optimize the allocation efficiency of the domestic capital market and attract international capital inflow (Geng and Farouk 2021). The linkage effect between different stock markets is also a manifestation of global financial integration. This signifies that there is a synchronous change trend in the same or opposite direction in stock prices in different stock markets (Youssef, Mokni, and Ajmi 2021). Many historical financial events have verified this phenomenon, such as the 2008 U.S. subprime crisis. When a financial crisis occurs, the global economy is greatly affected (Allen 2016).

The primary objective of this study is to explore recent economic developments and their related impacts in China and the United States by studying the linkage of stock markets. This linkage effect has undergone many market and empirical tests and can accurately reflect the correlation between different assets in the market, thereby reflecting a country’s economic impact on other countries (regions) (Naik, Padhi, and Joseph McCarthy 2015). Therefore, with the increasingly important role and status of China and the United States, studying the linkage effects between these two markets and other global stock markets is of great significance to investors. It can not only help investors better understand the operating mechanism of global stock markets but also help them formulate more effective investment strategies and achieve risk diversification. In addition, with the continuous emergence and development of related research methods, we have more tools and means to delve into this issue. Therefore, it is believed that through the study of the linkage effects of US and Chinese stock markets, we can make more valuable discoveries and provide more useful guidance for global investors.

Our research selects a time span from November 25, 2011, to July 5, 2023, covering the stock market indices of nine countries (or regions), and calculates the daily returns of these indices. When establishing the model, we add an exogenous variable, the VIX index, that can reflect the volatility of the global financial market and then apply the nonlinear Granger causality detection method to conduct a deeper study on the status and role of China and the United States in the linkage of stock markets. The results show that the United States, as the world’s largest economy, plays a leading role in the linkage of stock markets, and its stock market fluctuations have a significant impact on the changes in stock index returns in other countries. The stock index returns of China are the nonlinear Granger causes of all countries/regions except the United States, which indicates that China’s stock market has a certain impact on most stock market countries (or regions), but it cannot affect the US stock market. In addition, fluctuations in global stock markets will also impact the stock markets of China and the United States.

Our research makes contributions in three aspects. First, the paper conducts a deeper study on the status and role of China and the United States in the linkage of stock markets through empirical analysis, providing valuable reference information for investors, helping them better understand the operating mechanism of global stock markets, and formulating more effective investment strategies. Second, most previous studies have studied the linkage between countries (or regions) through the size of the correlation coefficient between stock markets and Granger causality. However, these methods have some limitations. On the one hand, the size of the correlation coefficient can only explain the strength of the linkage relationship but cannot clearly define the direction of volatility transmission between stock markets in countries (or regions); on the other hand, most financial asset price dynamics have nonlinear characteristics, and linear Granger methods cannot study nonlinear relationships between variables and effectively interpret their results. This paper seeks a method that can better analyze the direction of volatility transmission in the linkage between stock markets for research, making the model more effective and accurate. Finally, this paper supplements the literature on the linkage of stock markets, further enriching our understanding of stock market dynamics, mutual influences between markets, and the operating mechanism of global financial markets. These new research results provide new perspectives and directions for future academic research and provide valuable reference information for investors and policy makers.

The rest of this paper is organized as follows. Section 2 mainly introduces the VAR model and research methods used in this paper. Section 3 presents the data and empirical analysis process of the research, as well as the related results. Section 4 is the induction and summary of the research conclusions of this paper.

2. Methodology

There are many ways to measure market linkages, and a common method is to use vector autoregressive (VAR) models. This was a new macroeconometric framework proposed by Sims (1980). VAR models can capture the rich dynamics in multiple time series, providing a coherent and credible method for data description, prediction, structural inference, and policy analysis (Wu and Zhou 2014).

First, to study the impact of China and the United States on the world economy, we focus on the daily returns of the S&P 500 index in various countries and establishes a bivariate VAR model. This is because daily returns provide more data points and can better capture market dynamics. In addition, daily returns can better reflect short-term market fluctuations and provide more information. The S&P 500 index is a widely used benchmark that is often used to measure the overall economic situation. In terms of data selection, the sample period of this paper is from November 25, 2011, to July 5, 2023, covering major financial events such as Brexit, the China‒US trade war, and the COVID-19 pandemic. This ensures the timeliness of the research and makes the “China‒US factor” more representative in cross-national linkages.

Second, when establishing a bivariate VAR model to estimate the mutual influence relationship between US and Chinese stock index returns and other countries’ (or regions’) stock index returns, we add an exogenous variable VIX index that reflects global financial market volatility. This makes the model more effective and accurate when establishing the interaction relationship between China and the United States with other stock markets during shock or volatile periods. Because the VIX index is a mature index and easy to obtain, it has undergone many market tests. Many scholars (Moran and Liu, 2020) believe that the VIX index is an important indicator for measuring US stock market volatility and returns, and through the US stock market, it can reflect the global stock market situation to a certain extent.

To study the relationships between various variables more accurately and effectively, we use the VAR model for linear evaluation and uses the BDS test and RESET test to confirm the nonlinear part in the model, as well as the nonlinear Granger causality test method created by Hiemstra and Jones (1994). In addition, we also adopted the nonparametric Tn test statistic proposed by Diks and Panchenko (2006) to compensate for the defect of overrejection in this test method. At the same time, to ensure the robustness of the results of this test method, we also conducted an HJ test.

3. Empirical Analysis

3.1. Data and Descriptive Statistics

The data used in this article mainly include the VIX panic index and stock indices of various countries and regions. Considering factors such as the degree of market openness, comprehensive national strength, and the influence of the stock market in various countries and regions and referring to previous research, this article selects the following indices for analysis and research: the S&P 500 Index (SPX) of the United States, the Nikkei 225 Index (N225) of Japan, the Korean Index (KS11) of South Korea, the Russian Index (RTS) of Russia, the French CAC40 Index (FCHI), the Kuala Lumpur Index (KLSE) of Malaysia, the Mumbai Sensex Index (SENSEX) of India, the Shanghai Stock Exchange Index (SZZS) of China, and the Hang Seng Index (HSI) of Hong Kong, China. Based on data availability, the sample time span for empirical analysis in this article is from November 25, 2011, to July 5, 2023. The aforementioned stock indices and the VIX index daily closing prices are selected and converted into daily returns, which are calculated as follows:

(1) $R_t=100\times \left(\mathit{ln}{p}_t-\mathit{ln}{p}_{\mathit{t}-1}\right)$(1)

After preliminary analysis of the data, a total of 3051 observations of effective data were selected for the VIX index and stock index daily returns. The sample intervals and data sources as well as the related descriptive statistical results are shown in Tables 1 and 2.

Table 1. Sample intervals and data sources.

Variables	Frequency	Sample Interval	Sample Size	Sample Source
VIX	Daily Frequency	2011/11/25–2023/7/5	3051	Investing Database
SPX	Daily Frequency	2011/11/25–2023/7/5	3051	Wind Database
SZZS	Daily Frequency	2011/11/25–2023/7/5	3051	Wind Database
N225	Daily Frequency	2011/11/25–2023/7/5	3051	Wind Database
HSI	Daily Frequency	2011/11/25–2023/7/5	3051	Wind Database
KS11	Daily Frequency	2011/11/25–2023/7/5	3051	Wind Database
FCHI	Daily Frequency	2011/11/25–2023/7/5	3051	Wind Database
RTS	Daily Frequency	2011/11/25–2023/7/5	3051	Wind Database
SENSEX	Daily Frequency	2011/11/25–2023/7/5	3051	Wind Database
KLSE	Daily Frequency	2011/11/25–2023/7/5	3051	Wind Database

Table 2. Descriptive statistics.

Variables	Mean	Standard Deviation	Minimum	Maximum	Skewness	Kurtosis	KS P-value
VIX	−0.137	7.385	−29.98	76.82	1.241	10.852	.000
SPX	0.045	1.041	−12.77	8.97	−0.839	21.128	.000
SZZS	0.008	1.198	−8.87	5.6	−0.918	11.238	.000
N225	0.047	1.193	−8.25	7.81	−0.205	8.443	.000
HSI	0.001	1.163	−6.57	8.69	0.061	7.579	.000
KS11	0.014	0.919	−8.77	8.25	−0.226	12.171	.000
FCHI	0.034	1.182	−13.1	8.06	−0.683	13.113	.000
RTS	0.006	1.764	−18.24	13.29	−0.804	14.552	.000
SENSEX	0.046	0.985	−14.1	6.75	−1.423	23.849	.000
KLSE	0.005	0.610	−5.4	6.63	−0.151	14.159	.000

From the summary statistics in Table 2, the mean values of the daily stock index returns of various countries and regions are all positive except for the VIX index daily return, which is negative, and the average daily return values are very small. In terms of daily return volatility, the VIX index has the largest standard deviation (7.385) and stronger volatility. Comparatively, the standard deviations of daily returns of various stock indices are smaller (approximately 1%) and have weaker volatility.

In terms of the distribution, the skewness of the VIX index is 1.24, which is positive, indicating that the distribution of VIX index returns is right-skewed. In contrast, the skewness of stock index returns in nine countries and regions are all less than 0, except for the Hang Seng Index, indicating that their distributions are left-skewed. Further observation shows that the kurtosis coefficients of all return series are greater than 7 and significantly not equal to 0, so there are leptokurtic characteristics in both the VIX index and stock index return distributions. In addition, the p values of the KS test are all 0, indicating that neither the VIX index returns nor the stock index returns follow a normal distribution.

Table 3 shows the unconditional correlation analysis between the returns of the S&P 500 index in the United States, the Shanghai Composite Index in China, and the index returns of other countries (or regions). The results indicate that the highest correlation coefficient between the United States and France is 0.579. Moreover, compared to China, the correlation coefficients between the United States and other countries (or regions) are higher, meaning that SPX has the greatest association with other variables. In addition, among the unconditional correlation test results between the Shanghai Composite Index returns and the index returns of other countries (or regions), the correlation coefficient between the Hang Seng Index and the Shanghai Composite Index is the largest, indicating that China has the strongest association with Hong Kong’s stock market, which is consistent with reality. The results of unconditional correlation tests can only show that there is a correlation between the stock markets of the United States, China, and other countries (or regions) but cannot determine the direction of volatility transmission between stock markets.

Table 3. Unconditional correlation test.

Variables	SPX	SZZS	N225	HSI	KS11	FCHI	RTS	SENSEX	KLSE
SPX	1	0.1312	0.1823	0.1944	0.2194	0.5797	0.3079	0.2995	0.1287
SZZS	.1312	1	0.2661	0.5368	0.3184	0.1603	0.1354	0.2073	0.1842

Note: The table displays Pearson correlation based on daily observations, with a sample interval from November 25, 2011, to July 5, 2023.

3.2. Stationarity Test of the Return Rate Sequence

The ADF test of VIX index returns and stock index returns is shown in Table 4:

Table 4. ADF unit root test results and conclusions.

Variables	Z-valuc	1% Critical Value	5% Critical Value	P-valuc	Stationmrity
SPX	−57.693	−3.43	−2.86	.000	Stationary
SZZS	−52.157	−3.43	−2.86	.000	Stationary
N225	−51.123	−3.43	−2.86	.000	Stationary
KS11	−50.769	−3.43	−2.86	.000	Stationary
RTS	−50.627	−3.43	−2.86	.000	Stationary
FCHI	−51.564	−3.43	−2.86	.000	Stationary
KLSE	−50.112	−3.43	−2.86	.000	Stationary
SENSEX	−53.966	−3.43	−2.86	.000	Stationary
HSI	−51.768	−3.43	−2.86	.000	Stationary
VIX	−56.038	−3.43	−2.86	.000	Stationary

According to the results of the unit root test in Table 4, the statistical t values of the VIX index returns, SPX index returns, SZZS index returns, N225 index returns, HSI index returns, KS11 index returns, FCHI index returns, RTS index returns, SENSEX index returns and KLSE index returns are −56.038, −57.693, −52.157, −51.123, −51.768, −50.769, −51.564, −50.627, −53.966 and −50.112, respectively, which are all significantly lower than the critical value of −3.43 at the 1% confidence level, and the p values are all 0. Therefore, the null hypothesis is not accepted, which means that there is no unit root in the return series and that it is a stationary sequence variable.

3.3. Nonlinear Test of Residual Sequence

Before conducting research on the nonlinear Granger causality relationship between the stock market returns of China, the United States, and various countries (or regions), to ensure the robustness of the results, a nonlinear test must be conducted to examine whether there are significant nonlinear dynamic changes between China and the United States and other countries (or regions).

This paper uses two test methods, the BDS test and the RESET test, to test the nonlinearity of the residual sequence obtained by removing the linear relationship through the optimal bivariate VAR model and the exogenous variable VIX index. Table 5 shows the test results.

Table 5. Nonlinear test of interdependencies in stock index returns the US vs. other countries/regions.

	BDS Test	RESET Test	BDS Test	RESET Test
Regression of SPX Returns on Other Countries/Regions in a VAR System
SPX vs SZZS	17.65*	1.03	11.24*	1.09*
SPX vs N225	17.47*	1.031*	11.22*	1.20*
SPX vs HSI	17.28*	1.02*	8.35*	1.13*
SPX vs KS11	17.00*	1.02*	6.68*	0.91*
SPX vs FCHI	17.01*	0.85*	12.31*	0.96*
SPX vs RTS	17.50*	0.98*	9.45*	1.59*
SPX vs SENSEX	16.83*	0.99*	8.78*	0.89*
SPX vs KLSE	17.45*	1.03*	10.98*	0.59*
Regression of SZZS Returns on Other Countries/Regions in a VAR System
SZZS vs SPX	11.24*	1.09*	17.65*	1.03*
SZZS vs N225	11.21*	1.06*	9.13*	1.17*
SZZS. vs HSI	11.55*	2.72*	7.22*	0.96*
SZZS vs KS11	11.51*	1.04*	8.97*	0.88*
SZZS vs FCHI	11.13*	1.08*	14.47*	1.12
SZZS vs RTS	11.35*	1.08*	9.6*	1.16*
SZZS vs SENSEX	11.40*	1.07*	9.53*	0.91*
SZZS vs KLSE	11.69*	0.85*	12.68*	0.53

1. The regression residuals of SPX returns refer to the regression model obtained by using SPX as the dependent variable in the bivariate VAR model with the exogenous variable VIX index; the regression residuals of other countries’(regions’) returns refer to the regression model obtained by using the stock index returns of other countries (regions) as the dependent variable in the bivariate VAR model with the exogenous variable VIX index.

2. This paper uses the AIC information criterion to determine the optimal lag order of each bivariate VAR model.

Note: *indicate significance at the 5% significance levels.

The results show that all test statistics are significant at the 95% confidence interval, indicating that we do not accept the linear null hypothesis. Therefore, we can conclude that there is a significant nonlinear dynamic change trend in the mutual influence of the stock index returns of the United States and China on the stock index returns of other countries (or regions). This indicates that linear Granger cannot explain the model well. Therefore, we use nonlinear Granger causality analysis to further explore the nonlinear causal relationship in the model.

3.4. Nonlinear Granger Causality Test

3.4.1. The Causal Relationship Between the Stock Index Returns of the United States and Other Countries (Or Regions)

Table 6 lists the results of all HJ tests and Tn statistical tests. According to the results, the HJ test and Tn statistical test results of 1–8 orders are very robust, and the results of the nonparametric Tn statistical test and HJ test are consistent. We can analyze the nonlinear Granger causality between the stock index returns of the United States and other countries (or regions) through the results shown in the table above. Under the null hypothesis that there is no one-way nonlinear Granger causality between the SPX index returns and other countries’ (or regions’) index returns, this paper finds that the stock index returns of all countries (or regions) do not accept the null hypothesis at a significance level of 5% or 10%, which means that in the nonlinear transmission process of volatility between stock markets, American stock index returns are nonlinear Granger causes of stock index returns in China, Japan, Hong Kong, South Korea, France, Russia, India, and Malaysia. Therefore, the volatility of the American stock market will have a very significant impact on other countries’ (or regions’) stock markets. The results show that the American stock market has strong predictability for global stock markets; that is, the volatility of the American stock market is an important factor leading to global stock market volatility. In addition, by comparison, this paper finds that South Korea, France, Hong Kong and Russia have significant levels at 1%, which means that the impact of American stock market volatility on these countries is more significant.

Table 6. Nonlinear Granger causality test based on VAR linear filtering United States vs. other countries/regions.

Null Hypothesis: Stock index return s of the United States do not have nonlinear Granger causalityon the stock index return s of other countries/regions.
	SZZS		N225		HSI		KS11
LX = LY	Tn Test	HJ Test	Tn Test	HJ Test	Tn Test	HJ Test	Tn Test	HJ Test
1	2.228913*	2.213222*	2.701796*	2.710515*	4.035338*	3.988360*	4.417025*	4.335948*
	(0.012910)	(0.013441)	(0.003448)	(0.003359)	(0.000027)	(0.000033)	(0.000005)	(0.000007)
2	1.029114	1.052938	2.999122*	3.094905*	4.502535*	4.530475*	4.435225*	4.411633*
	(0.151713)	(0.146185)	(0.001354)	(0.000984)	(0.000003)	(0.000003)	(0.000005)	(0.000005)
3	1.824689*	1.868575*	2.265135*	2.457488*	4.461174*	4.757110*	4.404605*	4.608893*
	(0.034024)	(0.030841)	(0.011752)	(0.006996)	(0.000004)	(0.000001)	(0.000005)	(0.000002)
4	1.514666	1.568865	1.365270	1.588147	4.985404*	5.453110*	4.348247*	4.633454*
	(0.064929)	(0.058340)	(0.086084)	(0.056127)	0.000000	0.000000	(0.000007)	(0.000002)
5	2.117778	2.229234*	2.059566*	2.329622*	4.822533*	5.349436*	4.349372*	4.761034*
	(0.017097)	(0.012899)	(0.019720)	(0.009913)	(0.000001)	0.000000	(0.000007)	(0.000001)
6	2.482079*	2.642691*	2.099549*	2.354469*	4.190636*	4.750929*	4.215232*	4.697398*
	(0.006531)	(0.004113)	(0.017884)	(0.009275)	(0.000014)	(0.000001)	(0.000012)	(0.000001)
7	2.424976*	2.573800*	2.014617*	2.275444*	3.950190*	4.532656*	3.810163*	4.304680*
	(0.007655)	(0.005029)	(0.021972)	(0.011440)	(0.000039)	(0.000003)	(0.000069)	(0.000008)
8	2.072523*	2.222385*	2.050159*	2.365443*	3.796580*	4.498004*	3.729133*	4.310146*
	(0.019108)	(0.013129)	(0.020174)	(0.009004)	(0.000073)	(0.000003)	(0.000096)	(0.000008)
	FCHI		RTS		SENSEX		KLSE
LX = LY	Tn Test	HJ Test	Tn Test	HJ Test	Tn Test	HJ Test	Tn Test	HJ Test
1	4.614602*	4.513046*	3.547637*	3.605159*	2.972888*	3.090779*	2.972888*	3.090779*
	(0.000002)	(0.000003)	(0.000194)	(0.000156)	(0.001475)	(0.000998)	(0.001475)	(0.000998)
2	5.191077*	5.065148*	4.227913*	4.281681*	3.838390*	3.885433*	3.838390*	3.885433*
	0.000000	0.000000	(0.000012)	(0.000009)	(0.000062)	(0.000051)	(0.000062)	(0.000051)
3	4.877294*	5.001454*	4.253267*	4.248705*	3.141494*	3.315944*	3.141494*	3.315944*
	(0.000001)	0.000000	(0.000011)	(0.000011)	(0.000840)	(0.000457)	(0.000840)	(0.000457)
4	4.246006*	4.459524*	3.433704*	3.272692*	2.734021*	3.008683*	2.734021*	3.008683*
	(0.000011)	(0.000004)	(0.000298)	(0.000533)	(0.003128)	(0.001312)	(0.003128)	(0.001312)
5	3.976933*	4.300583*	3.296246*	3.086220*	2.456454*	2.775603*	2.456454*	2.775603*
	(0.000035)	(0.000009)	(0.000490)	(0.001014)	(0.007016)	(0.002755)	(0.007016)	(0.002755)
6	3.771290*	4.078498*	3.239192*	3.017990*	2.128258*	2.493788*	2.128258*	2.493788*
	(0.000081)	(0.000023)	(0.000599)	(0.001272)	(0.016658)	(0.006319)	(0.016658)	(0.006319)
7	3.047584*	3.428759*	3.276723*	3.037966*	2.088852*	2.399351*	2.088852*	2.399351*
	(0.001153)	(0.000303)	(0.000525)	(0.001191)	(0.018361)	(0.008212)	(0.018361)	(0.008212)
8	2.960039*	3.311564*	3.094205*	2.817301*	1.894754*	2.161660*	1.894754*	2.161660*
	(0.001538)	(0.000464)	(0.000987)	(0.002421)	(0.029062)	(0.015322)	(0.029062)	(0.015322)

Note: *indicate significance at the 5% significance levels.

As the world’s largest country, America has a high degree of trade relevance and financial relevance with many countries. America plays an important role in crisis contagion. As a weathervane for global stock markets, American stocks have a strong influence on global markets. Short-term rises and falls in American stocks will affect global market risk preferences. This is consistent with the existing research. For example, pointed out that the United States has a high degree of trade relevance and financial relevance with many countries (Baily and Elliott 2013).

3.4.2. The Causal Relationship Between the Stock Index Returns of Other Countries (Or Regions) and the United States

Table 7 lists the results of all HJ tests and Tn statistical tests. According to the results, the HJ test and Tn statistical test results of 1–8 orders are very robust, and the results of the nonparametric Tn statistical test and HJ test are consistent. It is found that there is no one-way nonlinear Granger causality between the index returns of other countries (or regions) and SPX index returns under the null hypothesis; China’s stock index returns do not accept the null hypothesis at the 5% significance level, which indicates that in the process of nonlinear transmission of volatility between stock markets, China’s stock index returns are nonlinear Granger causes of American stock index returns. This suggests that the Chinese stock market is unable to influence the United States, but fluctuations in the US stock market can be clearly transmitted to the Chinese stock market. The reason is likely because the Chinese stock market is still in its early stages of development and is not yet mature, with characteristics such as sharp rises and falls, and it is being influenced by external markets (mainly the US stock market).

Table 7. Nonlinear Granger causality test based on VAR linear filtering of other countries/regions vs. The United States.

Null Hypothesis: Stock index returns of other countries/regions do not have nonlinear Granger causality on the stock index returns of the United States.
	SZZS		N225		HSI		KS11
LX = LY	Tn Test	HJ Test	Tn Test	HJ Test	Tn Test	HJ Test	Tn Test	HJ Test
1	0.949036	1.030687	2.000013*	2.014912*	4.754640*	4.691695*	5.738319*	5.576957*
	(0.171301)	(0.151344)	(0.022749)	(0.021957)	(0.000001)	(0.000001)	0.000000	(0.000007)
2	0.365282	0.418560	2.902103*	2.850565*	5.807319*	5.607485*	6.609305*	6.179447*
	(0.357450)	(0.337769)	(0.001853)	(0.002182)	0.000000	0.000000	0.000000	(0.000005)
3	0.360109	0.417041	1.905516*	1.898949*	4.617074*	4.637958*	5.993064*	5.878109*
	(0.359383)	(0.338324)	(0.028357)	(0.028786)	(0.000002)	(0.000002)	0.000000	0.000000
4	0.347304	0.306914	1.391208	1.362028	4.119097*	4.211148*	5.134006*	5.287338*
	(0.635818)	(0.620546)	(0.082081)	(0.086595)	(0.000019)	(0.000013)	0.000000	0.000000
5	0.079329	0.036469	1.118027	1.073633	3.541206*	3.630103*	4.634992*	4.909779*
	(0.531615)	(0.514546)	(0.131778)	(0.141494)	(0.000199)	(0.000142)	(0.000002)	0.000000
6	614904	0.610463	1.431681	1.413610	3.681515*	3.746678*	4.857715*	5.256148*
	(0.730691)	(0.729222)	(0.076118)	(0.078738)	(0.000116)	(0.000090)	(0.000001)	0.000000
7	1.042650	1.028439	1.027757	1.063067	2.760546*	2.827672*	4.534896*	5.014239*
	(0.851445)	(0.848128)	(0.152032)	(0.143876)	(0.002885)	(0.002344)	(0.000003)	0.000000
8	0.850180	1.028439	0.830763	0.893566	2.343984*	2.392966*	4.132408*	4.598228*
	(0.802388)	(0.848128)	(0.203054)	(0.185777)	(0.009540)	(0.008356)	(0.000018)	(0.000002)
	FCHI		RTS		SENSEX		KLSE
LX = LY	Tn Test	HJ Test	Tn Test	HJ Test	Tn Test	HJ Test	Tn Test	HJ Test
1	3.723203*	3.883237*	3.517192*	3.560033*	3.893293*	3.807330*	3.733234*	3.724451*
	(0.000098)	(0.000052)	(0.000218)	(0.000185)	(0.000049)	(0.000070)	(0.000095)	(0.000098)
2	5.628690*	5.523708*	3.644399*	3.644761*	3.068236*	3.076789*	3.964173*	3.966853*
	0.000000	0.000000	(0.000134)	(0.000134)	(0.001077)	(0.001046)	(0.000037)	(0.000036)
3	5.356640*	5.302640*	3.689210*	3.672717*	2.868449*	2.804524*	4.080792*	4.070039*
	0.000000	0.000000	(0.000112)	(0.000120)	(0.002062)	(0.002520)	(0.000022)	(0.000024)
4	4.627779*	4.721915*	3.734462*	3.787298*	2.661502*	2.645890*	3.670935*	3.708244*
	(0.000002)	(0.000001)	(0.000094)	(0.000076)	(0.003890)	(0.004074)	(0.000121)	(0.000104)
5	4.558104*	4.687887*	3.772618*	3.844846*	2.333509*	2.228143*	3.439206*	3.557887*
	(0.000003)	(0.000001)	(0.000081)	(0.000060)	(0.009811)	(0.012935)	(0.000292)	(0.000187)
6	4.119097*	4.229905*	3.161991*	3.204933*	2.073784*	1.921667*	2.957213*	3.124084*
	(0.000019)	(0.000012)	(0.000783)	(0.000675)	(0.019050)	(0.027324)	(0.001552)	(0.000892)
7	3.327327*	3.540230*	3.108306*	3.141371*	2.165011*	2.015823*	2.245462*	2.377117*
	(0.000438)	(0.000200)	(0.000941)	(0.000841)	(0.015193)	(0.021909)	(0.012369)	(0.008724)
8	3.375192*	3.618566*	2.646659*	2.679413*	2.223287*	2.077066*	2.142801*	2.301877*
	(0.000369)	(0.000148)	(0.004065)	(0.003688)	(0.013098)	(0.018898)	(0.016065)	(0.010671)

Note: ** and * indicate that the null hypothesis of “no existence of nonlinear Granger causality” is rejected at the significance level s of 1%,5%, and 10%, respectively.

On the other hand, stock market fluctuations in countries other than China can have an impact on the US stock market. This is perhaps due to the close economic ties between the US and other countries, where investment, trade, and monetary policy in other countries can affect the US economy. For example, Malaysia and the United States maintain good cooperation in areas such as economics, investment, health, and defense (Congressional Research Service 2017). In addition, the United States is one of Malaysia’s largest investors, and investment in other countries is likely to change investors’ perceptions of companies and industries, thereby affecting the stock market.

3.4.3. The Causal Relationship Between the Stock Index Returns of China and Other Countries (Or Regions)

Table 8 lists the results of all HJ tests and Tn statistical tests, and we can analyze the nonlinear Granger causality relationship between China’s stock index returns and other countries (or regions) through the results shown in the table. According to the results, the HJ test and Tn statistical test results of 1–8 orders are very robust, and the results of the nonparametric Tn statistical test and HJ test are consistent. Under the null hypothesis that there is no one-way nonlinear Granger causality between SZZS index returns and other countries’ (or regions’) index returns, this study found that the t-statistics of US stock index returns are not significant at the 5% significance level, which means that in the nonlinear transmission process of volatility between stock markets, China’s stock market index returns are not the nonlinear Granger cause of US stock index returns; that is, China’s stock market volatility does not have a significant impact on US and French stock markets. The main reason is that China’s stock market is not synchronized with European and American stock markets, coupled with the fact that European and American stock markets are relatively mature, and currently China’s stock market volatility does not have a significant impact on them. At the same time, the t-statistics of other countries’ (or regions’) stock index returns do not accept the null hypothesis at the 5% significance level except in the cases of the United States and France; that is, in the nonlinear transmission process of volatility between stock markets, China’s stock market index returns are the nonlinear Granger cause of Japan, Hong Kong, South Korea, Russia, India, and Malaysia stock index returns. Therefore, China’s stock market volatility has a significant impact on these countries’ (or regions’) stock markets (which all belong to Asian markets). This is consistent with current reality. In terms of trade exchanges and market expectations in Asian markets, China maintains a high degree of relevance with these countries in terms of capital flows. In addition, China and France maintain a strong economic partnership, with rapid mutual investment growth in various industries, such as agriculture, industry, transportation, urban development, large-scale retail, and finance (Duggal 2022).

Table 8. Nonlinear Granger causality test based on VAR linear filtering for China vs. other countries/regions.

Null Hypothesis: Stock index returns of China do not have nonlinear Granger causality on the stock index returns of other countries/regions.
	SPX		N225		HSI		KS11
LX = LY	Tn Test	HJ Test	Tn Test	HJ Test	Tn Test	HJ Test	Tn Test	HJ Test
1	0.949036	1.030687	2.610222*	2.652412*	1.902864*	1.982156*	2.413177*	2.522788*
	(0.171301)	(0.151344)	(0.004524)	(0.003996)	(0.028529)	(0.023731)	(0.007907)	(0.005821)
2	0.365282	0.418560	3.708878*	3.817146*	1.240716	1.413345	2.643856*	2.753457*
	(0.357450)	(0.337769)	(0.000104)	(0.000068)	(0.107355)	(0.078777)	(0.004098)	(0.002948)
3	0.360109	0.417041	3.357642*	3.544465*	1.267790	1.412494	2.350517*	2.442023*
	(0.359383)	(0.338324)	(0.000393)	(0.000197)	(0.102436)	(0.078902)	(0.009374)	(0.007303)
4	(0.347304)	(0.306914)	2.947665*	3.215085*	1.384633	1.561060	1.363660	1.449031
	(0.635818)	(0.620546)	(0.001601)	(0.000652)	(0.083082)	(0.059255)	(0.086337)	(0.073664)
5	(0.079329)	(0.036469)	3.336600*	3.704138*	1.825878*	2.014723*	1.774478*	1.892667*
	(0.531615)	(0.514546)	(0.000424)	(0.000106)	(0.033934)	(0.021967)	(0.037992)	(0.029201)
6	(0.614904)	(0.610463)	2.886051*	3.297946*	1.387995	1.543101	1.840831*	1.962262*
	(0.730691)	(0.729222)	(0.001951)	(0.000487)	(0.082569)	(0.061403)	(0.032823)	(0.024866)
7	(1.042650)	(1.028439)	2.391374*	2.733862*	1.389774	1.499622	1.591918	1.691123*
	(0.851445)	(0.848128)	(0.008393)	(0.003130)	(0.082299)	(0.066856)	(0.055702)	(0.045407)
8	(0.850180)	(0.834493)	1.986599*	2.347051*	1.101419	1.198550	1.068660	1.128982
	(0.802388)	(0.797998)	(0.023483)	(0.009461)	(0.135357)	(0.115351)	(0.142611)	(0.129453)
	FCHI		RTS		SENSEX		KLSE
LX = LY	Tn Test	HJ Test	Tn Test	HJ Test	Tn Test	HJ Test	Tn Test	HJ Test
1	3.087565*	3.155178*	2.001585*	2.057836*	2.500047*	2.554349*	3.162650*	3.167223*
	(0.001009)	(0.000802)	(0.022665)	(0.019803)	(0.006209)	(0.005319)	(0.000782)	(0.000770)
2	3.296306*	3.458224*	3.041648*	3.130802*	1.844467*	1.971432*	3.868491*	3.913040*
	(0.000490)	(0.000272)	(0.001176)	(0.000872)	(0.032558)	(0.024337)	(0.000055)	(0.000046)
3	2.986748*	3.241532*	2.835520*	3.006592*	1.699515*	1.837375*	3.541752*	3.683588*
	(0.001410)	(0.000594)	(0.002288)	(0.001321)	(0.044611)	(0.033077)	(0.000199)	(0.000115)
4	3.373289*	3.706103*	2.505884*	2.746431*	2.227666*	2.323605*	3.046003*	3.252782*
	(0.000371)	(0.000105)	(0.006107)	(0.003012)	(0.012951)	(0.010073)	(0.001160)	(0.000571)
5	3.024437*	3.498515*	2.317820*	2.539319*	2.577873*	2.756277*	2.891515*	3.313772*
	(0.001245)	(0.000234)	(0.010230)	(0.005553)	(0.004971)	(0.002923)	(0.001917)	(0.000460)
6	2.639257*	3.136830*	2.149635*	2.409103*	2.335553*	2.519095*	2.843760*	3.245400*
	(0.004154)	(0.000854)	(0.015792)	(0.007996)	(0.009757)	(0.005883)	(0.002229)	(0.000586)
7	2.313490*	2.786290*	1.864060*	2.143787*	2.034690*	2.317289*	2.631764*	3.148518*
	(0.010348)	(0.002666)	(0.031157)	(0.016025)	(0.020941)	(0.010244)	(0.004247)	(0.000821)
8	2.023587*	2.463629*	2.298345*	2.638775*	2.342222*	2.713079*	2.894230*	3.559574*
	(0.021506)	(0.006877)	(0.010771)	(0.004160)	(0.009585)	(0.003333)	(0.001900)	(0.000186)

Note: * indicate significance at the 5% significance levels.

3.4.4. The Causal Relationship Between the Stock Index Returns of Other Countries (Or Regions) and the Stock Index Returns of China

Table 9 lists the results of all HJ tests and Tn statistical tests, and we can analyze the nonlinear Granger causality relationship between China’s stock index returns and other countries (or regions) through the results shown in the table. According to the results, the HJ test and Tn statistical test results of 1–8 orders are very robust, and the results of the nonparametric Tn statistical test and HJ test are consistent. Under the null hypothesis that there is no one-way nonlinear Granger causality between SZZS index returns and other countries’ (or regions’) index returns, this study found that the t-statistics of all countries’ (or regions’) stock index returns do not accept the null hypothesis at the 5% significance level, which means that in the nonlinear transmission process of volatility between stock markets, all countries’ (or regions’) stock index returns are the nonlinear Granger cause of China’s stock index returns, which means that global stock market volatility is very likely to have an impact on China’s stock market. The main reason for this phenomenon is that China’s stock market is a bear-long bull-short cycle market, where most of the time, the A-share index is in a downward trend, in which all positive effects will be reduced and negative effects will be magnified. In addition, investors in China’s stock market are mainly composed of retail investors, and although their funds account for a small proportion, their emotions are easily influenced and are irrational (Lu and Junjie, 2014). Moreover, China’s stock market is not sufficiently mature, and external stock market volatility can easily affect China’s capital market and can impact China’s stock market.

Table 9. Nonlinear Granger causality test based on VAR linear filtering of other countries/regions vs. China.

Null Hypothesis:Stock index returns of other countries/regions do not have nonlinear Granger causality on the stock index returns of China
	SPX		N225		HSI		KS11
LX = LY	Tn Test	HJ Test	Tn Test	HJ Test	Tn Test	HJ Test	Tn Test	HJ Test
1	2.228913*	2.213222	2.942526*	2.921653*	1.310104	1.339329	2.826887*	2.852609*
	(0.012910)	(0.013441)	(0.001628)	(0.001741)	(0.095080)	(0.090232)	(0.002350)	(0.002168)
2	1.029114	1.052938	2.567975*	2.615689*	2.074450*	2.098682*	2.458324*	2.659371*
	(0.151713)	(0.146185)	(0.005115)	(0.004452)	(0.019019)	(0.017922)	(0.006979)	(0.003914)
3	1.824689*	1.868575	1.454354	1.534602	1.584992	1.707762*	1.573313	1.791737*
	(0.034024)	(0.030841)	(0.072924)	(0.062441)	(0.056484)	(0.043840)	(0.057823)	(0.036588)
4	1.514666	1.568865	0.731139	0.822562	0.427313	0.551632	0.978381	1.191816
	(0.064929)	(0.058340)	(0.232347)	(0.205379)	(0.334576)	(0.290600)	(0.163943)	(0.116667)
5	2.117778*	2.229234	0.723441	0.803897	0.465893	0.611112	0.811125	1.062851
	(0.017097)	(0.012899)	(0.234704)	(0.210728)	(0.320646)	(0.270563)	(0.208647)	(0.143925)
6	2.482079*	2.642691	1.755720*	1.960541*	1.164528	1.269229	0.882490	1.152839
	(0.006531)	(0.004113)	(0.039568)	(0.024966)	(0.122105)	(0.102180)	(0.188756)	(0.124488)
7	2.424976*	2.573800	1.973873*	2.152292*	0.773977	0.853140	1.110608	1.346273
	(0.007655)	(0.005029)	(0.024198)	(0.015687)	(0.219472)	(0.196791)	(0.133369)	(0.089107)
8	2.072523*	2.222385	2.091073	2.375159*	0.417225	0.544026	1.064854	1.281248
	(0.019108)	(0.013129)	(0.018261)	(0.008771)	(0.338257)	(0.293212)	(0.143471)	(0.100053)
	FCHI		RTS		SENSEX		KLSE
LX = LY	Tn Test	HJ Test	Tn Test	HJ Test	Tn Test	HJ Test	Tn Test	HJ Test
1	4.405798*	4.420394*	3.005978*	2.988025*	2.685747*	2.746345*	3.080710*	3.131809*
	(0.000005)	(0.000005)	(0.001324)	(0.001404)	(0.003618)	(0.003013)	(0.001033)	(0.000869)
2	3.619742*	3.758391*	3.217897*	3.233363*	3.013411*	3.166884*	3.974011*	4.012217*
	(0.000147)	(0.000086)	(0.000646)	(0.000612)	(0.001292)	(0.000770)	(0.000035)	(0.000030)
3	3.351213*	3.564303*	3.397710*	3.505973*	2.641067*	2.823704*	3.507670*	3.608987*
	(0.000402)	(0.000182)	(0.000340)	(0.000227)	(0.004132)	(0.002374)	(0.000226)	(0.000154)
4	3.602114*	3.965594*	3.694434*	3.835024*	2.750995*	2.963542*	2.801502*	2.996570*
	(0.000158)	(0.000037)	(0.000110)	(0.000063)	(0.002971)	(0.001521)	(0.002543)	(0.001365)
5	3.735672*	4.316976*	3.578579*	3.869715*	2.631434*	2.875686*	2.684058*	2.928476*
	(0.000094)	(0.000008)	(0.000173)	(0.000054)	(0.004251)	(0.002016)	(0.003637)	(0.001703)
6	3.754601*	4.481130*	3.929311*	4.524838*	3.392330*	3.766022*	2.568708*	2.844143*
	(0.000087)	(0.000004)	(0.000043)	(0.000003)	(0.000347)	(0.000083)	(0.005104)	(0.002227)
7	3.871101*	4.773762*	4.066109*	4.855584*	3.075010*	3.554529*	2.133528*	2.381633*
	(0.000054)	(0.000001)	(0.000024)	(0.000001)	(0.001052)	(0.000189)	(0.016441)	(0.008618)
8	3.499035*	4.373062*	3.956244*	4.873808*	2.495499*	2.902389*	2.773134*	3.199237*
	(0.000233)	(0.000006)	(0.000038)	(0.000001)	(0.006289)	(0.001852)	(0.002776)	(0.000689)

Note: *indicate significance at the 5% significance levels.

4. Conclusion

In this study, we reveal the close connections and mutual influences of economies worldwide in the context of deepening globalization. Whether it is France and Russia in Europe or Japan, South Korea, and Malaysia in Asia, they all have a significant impact on the US stock market. This mutual influence is reflected not only in trade, investment, and finance but also in policy, technology, and cultural exchanges. Even a superpower such as the United States cannot avoid being influenced by other countries and multiple factors.

On the other hand, the volatility of China’s stock market has a certain impact on most stock market countries (or regions) but cannot affect the US stock market. However, the volatility of the global stock market is very likely to impact China’s stock market. This is mainly related to factors such as the immature development of China’s stock market and the fact that most investors in the stock market are individual investors.

In recent years, China’s stock market and economic development have progressed rapidly. Although China’s stock market cannot affect the US stock market, it can still have a transmission effect on most countries, indicating that China has a significant impact on the world economy. Since both China and the United States are the world’s largest economies, their trade relations have a significant impact on the global economy.

In summary, this study emphasizes the interdependence of economies in the context of globalization and highlights the important positions of China and the United States in the global economy. At the same time, it also reminds us that we should pay more attention to risk management related to policy changes associated with China’s rise, and countries worldwide need to strengthen cooperation to jointly address global challenges and promote the sustained and stable development of the world economy.

Acknowledgments

We would like to express our gratitude to everyone who has helped and supported us during this research.

First, we would like to thank Zhejiang University of Finance and Economics for providing financial support for this research.

Second, we would like to thank Bingkun Yang and Weihua Huang for providing valuable guidance and advice on this research.

Finally, we would like to thank all the volunteers who participated in this research. Without their support, this research would not have been possible.

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Data Availability Statement

VIX data used in this study comes from a public investing database, which can be freely accessed at https://www.investing.com. The other part of the data comes from the Wind database, which can be accessed through a subscription to the database. For detailed information on how to access these data, please refer to the relevant database websites.

Additional information

Funding

The author(s) reported there is no funding associated with the work featured in this article.