Do the RMB exchange rate and global commodity prices have asymmetric or symmetric effects on China’s stock prices?

With the rapid expansion of the RMB exchange rate’s floating range, the effects of the RMB exchange rate and global commodity price changes on China’s stock prices are likely to increase. This study uses both auto regressive distributed lag (ARDL) and nonlinear ARDL (NARDL) approaches to explore the symmetric and asymmetric effects of the RMB exchange rate and global commodity prices on China’s stock prices. Our findings show that without considering the critical variable of global commodity prices, there is no cointegration relationship between the RMB exchange rate and China’s stock prices, and the coefficient of the RMB exchange rate is not statistically significant. However, when we introduce global commodity prices into the NARDL model, the result shows that the RMB exchange rate has a negative effect on China’s stock prices, that there indeed exists a long-run cointegration relationship among the RMB exchange rate, global commodity prices, and stock prices in the NARDL model, and that global commodity price changes have an asymmetric effect on China’s stock prices in the long run. Specifically, China’s stock prices are more sensitive to increases than decreases in global commodity prices. Thus, increases in global commodity prices cause China’s stock prices to decline sharply. In contrast, the same magnitude of decline in global commodity prices induces a smaller increase in China’s stock prices.

growing number of researchers have tried to identify whether changes in exchange rates impact stock prices. However, the conclusions are still contested.
In studies on the impact of exchange rates on stock prices, an important recent finding is that the omission of global commodity prices, a critical variable, may lead to biased results. Furthermore, it is easy to overlook the relationship between the exchange rates and stock prices. As an essential input for industrial and agricultural production, changes in global commodity prices will inevitably affect the profits of enterprises, and such changes will eventually reflect in the stock market. The impact of global commodity prices on stock prices varies depending on whether a country is a commodity exporter or importer. For global commodity-exporting countries, the rise of global commodity prices brings more profits to their enterprises, leading to an increase in stock prices (Chortareas et al. 2011). However, for global commodity-importing countries, the effect may be the opposite. Higher global commodity prices can lead to higher production costs for domestic firms, weakening their profitability and negatively impacting stock prices (Jones et al. 2004). Meanwhile, as the financial attribute of global commodities strengthens, an increasing number of financial products are designed to target global commodities, which provides an investment alternative to stocks (Enilov et al. 2021). Because some global commodities and the financial products designed to target them are considered safe assets, investors shift investments over to commodities and their financial products when the economy and stocks are not doing well and vice-versa (Jain and Biswal 2016). Thus, there is greater substitutability between global commoditybased financial products and stocks due to the financialization of commodities. Changes in global commodity prices can affect investors' asset allocation, causing changes in demand for stocks and, consequently, stock prices as well.
We examine the impact of exchange rates and global commodity prices on stock prices in China, the largest developing country. Several reasons motivate our focus on the relationships among these variables. First, China's RMB exchange rate has become much more market-oriented, and its impact on the domestic stock market may increase significantly (Tian and Ma 2010;Nieh and Yau 2010;Rutledge et al. 2014). In July 2005, China began to implement a managed floating exchange rate regime, with the RMB exchange rate no longer pegged to the US dollar. The country formed a more flexible RMB exchange rate regime based on market supply and demand, adjusting for a basket of currencies. In 2014, the People's Bank of China expanded the floating range of the RMB exchange rate to US dollar, from 1 to 2%, further enhancing RMB bidirectional floating flexibility. Moreover, China has insisted on an export-oriented strategy for a long time; thus, the external dependence of the Chinese economy is relatively high. The expansion of the fluctuation range of the RMB exchange rate will inevitably affect imports and exports, thereby causing fluctuations in the stock market because of expected changes in companies' profitability.
Second, it is beneficial to study whether there is an asymmetric impact of the RMB exchange rate on stock prices in China. In the ongoing literature, the asymmetric effects of exchange rates on stock prices have been confirmed in many developed countries (Bahmani-Oskooee and Saha 2016). Nonetheless, this type of research on China is scarce. Given that firms may use real options to hedge the risks associated with exchange rate changes (Miller and Reuer 1998), the uncertainty of future cash flows, and the presence of default risk (Bartram 2004), the impact of exchange rates on enterprise performance and stock prices may be asymmetric. Therefore, it is necessary to investigate whether a similar asymmetric effect exists in China to better inform governments and investors' decision-making.
Third, China is a major importer of global commodities. By affecting the production costs and future cash flows of Chinese companies, changes in global commodity prices may indirectly affect company profits and stock prices. The global commodity market has long been monopolized by a small number of oligarchic companies (Meyer and Cramon-Taubadel 2010); however, China's industry concentration ratio is low compared to other developed economies. As such, it is difficult for Chinese companies to possess bargaining power over global commodities companies. 1 Thus, there may exist an asymmetric price transmission from global commodity prices to product costs for Chinese companies (Long and Liang 2018). That is, the impact of global commodity prices on enterprise profits and stock prices may be asymmetric.
As reform of the RMB exchange rate formation mechanism continues to deepen, along with China's high external dependence on global commodities, it is necessary to clarify the asymmetric impacts of the RMB exchange rate and global commodity prices on China's stock prices. Dramatic changes in stock prices not only have an adverse effect on the capital market, but also have a negative effect on the healthy development of the entire economy (Wen et al. 2019). Thus, this study's findings can help investors better understand and forecast changes in stock markets, make more profitable investments, and adopt appropriate hedging strategies when encountering RMB exchange rate and commodity price changes. Moreover, it is also crucial for authorities to more successfully stabilize China's stock market based on asymmetric influence characteristics.

The effects of exchange rates on stock prices
The debate about whether there is a relationship between exchange rates and stock prices has been ongoing for some time, but no consensus has been reached. Two main theoretical models attempt to account for the interaction between exchange rates and stock prices. One is the flow-oriented model, developed by Dornbusch and Fischer (1980), which asserts that a movement in a country's currency will change actual output and stock prices through products' global competitiveness and trade balance. The depreciation of domestic currency can lead to an increase in output and export via the dividend-discount model, which translates into a rise in stock prices with investors' optimistic expectations of company profitability. The other is the stock-oriented model, suggested by Branson (1983) and Frankel (1992), which proposes that exchange rates are affected by stock prices through capital mobility. Increasing domestic stock prices attract foreign capital to the domestic stock market, bringing appreciation pressure on domestic currency.
In empirical research, the literature on the relationship between exchange rates and stock prices is very extensive but remains controversial. On one hand, numerous empirical studies provide evidence favoring the flow-oriented hypothesis of exchange rates. The earliest study was conducted by Aggarwal (1981), who concluded that there is a positive relationship between the two variables using monthly data from 1974 to 1978 in the United States. Subsequently, many studies have supported the effect of exchange rates on stock prices using various empirical approaches, such as cointegration techniques, the Granger causality test, and so on (Phylaktis and Ravazzolo 2005;Yau and Nieh 2009;Aslam and Ramzan 2013;Lin and Fu 2016;Sui and Sun 2016;Yang 2017). On the other hand, numerous studies support the stock-oriented hypothesis of exchange rates (Soenen and Hennigar 1988;Maysami and Koh 2000;Wongbangpo and Sharma 2002;Kim 2003;Ibrahim and Aziz 2003;Tsai 2012;Inegbedion 2012;Liang et al. 2013). However, other studies either reveal that no apparent relationship exists between exchange rates and stock prices, or their results are ambiguous (Bahmani-Oskooee and Sohrabian 1992;Wu 2000;Nieh and Lee 2001;Smyth and Nandha 2003;Doong et al. 2005;Lean et al. 2005;Rahman and Uddin 2009;Zhao 2010;Kollias et al. 2012;Wickremasinghe 2012).
China has also aroused the interest of scholars on this issue. Several studies have focused on the impact of the RMB exchange rate on China's stock prices. Li and Huang (2008) found a short-run causation effect of the RMB exchange rate on Shanghai stock returns. Nieh and Yau (2010), Zhao (2010), Tian and Ma (2010), and Rutledge et al. (2014) also came to similar conclusions. Nevertheless, these studies on China are more straightforward and mainly examine the linear relationship between these variables. However, under different thresholds, the relationship between variables is usually nonlinear (Tian et al. 2020). Several recent studies have pointed out that the symmetry assumption may underestimate the impact of exchange rates on stock prices (Effiong and Bassey 2019;Wong 2019;Salisu et al. 2020). Ismail and Isa (2009) concluded that a nonlinear model is more appropriate. Applying a nonlinear model, they found a nonlinear relationship between exchange rates and stock prices in Malaysia using monthly data from 1990 to 2005. Bahmani-Oskooee and Saha (2015) also revealed that exchange rate changes have asymmetric effects on stock prices after introducing nonlinearity into the adjustment process. Ding (2021) pointed out that the relationship among exchange rates and stock prices is time-varying, so traditional linear models may not accurately capture the relationship. Therefore, in this study, we employ both the symmetric auto regressive distributed lag (ARDL) model and the asymmetric nonlinear auto regressive distributed lag (NARDL) model to analyze and compare the symmetric and asymmetric effects of the RMB exchange rate on China's stock prices to avoid estimation bias caused by model setting.

The effects of global commodity prices on stock prices
Although much research progress has been made on the effects of exchange rates on stock prices, several aspects remain worthy of further study. First, some studies lack the key variable of global commodity prices. As mentioned, global commodity prices significantly impact the input prices of products and the balance sheets of listed companies and their stock prices. Chaban (2009) discovered a three-way relationship among exchange rates, commodity prices, and stock prices. Basher et al. (2012) studied the dynamic linkage among exchange rates, oil price, and emerging market stock price and found that increases in oil prices tend to drive down emerging market stock prices in the short run. Chortareas et al. (2011) examined the role of oil prices from 1994 to 2006 for a possible link between exchange rates and the stock market for oil-exporting countries, such as Egypt, Kuwait, Oman, and Saudi Arabia. They also noted that, when the oil price is not considered, there is no long-run cointegration relationship between exchange rates and stock prices. However, when the oil price is considered, exchange rates are positively related to stock prices in Egypt and Oman. Groenewold and Paterson (2013) in a study on Australia from 1979 to 2010 revealed that the relationship between exchange rates and stock prices is weak when omitting global commodity prices. Nevertheless, once global commodity prices are added, all three variables are cointegrated in the long run. Roubaud and Arouri (2018) argue that exchange rates, oil prices, and stock markets should be linked theoretically, as oil plays an active role in the effect of exchange rates on stock prices. Akbar et al. (2019) examined and confirmed the dynamic linkages among exchange rates, gold prices, interest rates, and stock prices in Pakistan. Singhal et al. (2019) investigated and found a dynamic relationship among exchange rates, international oil prices, international gold prices, and stock market index in Mexico. Chkir et al. (2020) also studied the relationship among oil prices, exchange rates, and stock prices in Canada, Australia, Mexico, Norway, Britain, France, and Japan.
However, although research has been ample, few studies have focused on major importing countries such as India (Ram 2017;Kumar et al. 2020). Moreover, relatively few studies have examined the impact of the RMB exchange rate on China's stock prices while adding the variable of global commodity prices, which has proven unignorable in more recent studies. Given the high degree of dependence on global commodities imports, China must consider the impact of global commodity prices when investigating the relationship between exchange rates and stock prices.
Moreover, the impact of global commodity prices on stock prices may be asymmetric. Using a regime-switching approach, Roubaud and Arouri (2018) found relationships among oil prices, exchange rates, and stock markets to be nonlinear and asymmetric. Kumar (2019) also examined the asymmetric impact of oil prices on stock prices. The results demonstrated that positive (negative) shocks in oil prices have significant positive (negative) impacts on stock prices. Furthermore, a positive shock has a more pronounced effect than a negative shock. Chang (2020) examined the asymmetric impact of oil prices on stock prices and found that in the short run, oil prices significantly and asymmetrically affect stock prices in Russia, Indonesia, and India. Olayeni et al. (2020) also found that there is a long-run, asymmetric relationship among oil prices, exchange rates, global economic activity index, oil production, and stock market activity in Nigeria.
In general, existing literature on the impact of the RMB exchange rate on China's stock prices either ignores the vital variable of commodity prices or does not consider the asymmetry among these variables. Accordingly, this study attempts to overcome these shortcomings and makes marginal contributions to the previous literature in two aspects. First, we add global commodity prices and other primary macroeconomic variables when studying the relationships between the RMB exchange rate and China's stock prices to prevent omitting key variables. Second, using the NARDL model developed by Shin et al. (2014), we consider the asymmetric effects of the RMB exchange rate and global commodity prices on China's stock prices by relaxing the strict assumption of symmetry to capture a more reasonable and realistic relationship. For comparison, we also employ the ARDL model to investigate the symmetric relationship among these variables.
The remainder of this paper is organized as follows. Section "Methods and models" describes the methodology and data, section "Data and empirical results" presents and interprets the overall results, and section "Conclusion" draws conclusions and implications based on the findings.

Methods and models
We use both ARDL and NARDL models in this study. The ARDL model captures the symmetric relationship among these variables, while the NARDL helps analyze the asymmetric relationship between financial or economic time series (Katrakilidis and Trachanas 2012;Asimakopoulos et al. 2000), such as the exchange rates and stock prices. Compared with other conventional cointegration techniques, the NARDL model exhibits both cointegration and asymmetric nonlinearity in a single equation. Moreover, the model contains a dynamic error correction that captures both short-and long-run asymmetries (Shahzad et al. 2017). Thus, it can identify the asymmetric effects of the rise and fall of the RMB exchange rate and global commodity prices on China's stock prices in the short and long run. Furthermore, unlike standard cointegration techniques, the ARDL and NARDL models are flexible to different orders of integrations in the time series. They are applicable regardless of whether the regression variables are pure I(0), I(1), or mutually cointegrated (Pesaran et al. 2001;Shin et al. 2014).

Symmetry relationship in the linear ARDL framework
According to the number of variables in the estimated equation, existing research can be divided into two categories-the bivariate model, including only stock prices and exchange rate, and the multivariable model, including additional control variables (Bahmani-Oskooee and Saha 2015). According to Bahmani-Oskooee and Saha (2015), the multivariable model can prevent inaccurate estimation stemming from the omission of the main macroeconomic variables as in the bivariate model. As such, we adopt the revised multivariate model of Boonyanam (2014), Moore and Wang (2014), Bahmani-Oskooee and Saha (2015), and Bahmani-Oskooee and Saha (2016), among others, to estimate the relationship between the RMB exchange rate and stock prices: where sp denotes an index of China's stock prices, and neer denotes the nominal effective exchange rate of RMB 2 ; fr is the foreign exchange reserve; i is the interest rate, representing the price monetary policy instrument; m2 is a measure of the broad money supply that represents the quantitative monetary policy instrument and may have (1) sp t = β 0 + β 1 neer t + β 2 fr t + β 3 i t + β 4 ipi t + β 5 m2 t + µ t positive effects on the stock market; ipi is the industrial production index used as a proxy for domestic economic activities, which may also have a positive impact on stock prices; and µ is the random error term. All the variables are in logarithms except for interest rate i.
For comparison, we add the global commodity prices in Eq.
(1) to study its influence on China's stock prices because not including them may make the cointegration relationship between the RMB exchange rate and stock prices seem non-existent (Groenewold and Paterson, 2013). Thus, Eq. (1) can be rewritten as: where comm refers to global commodity prices and is also expressed in logarithmic form.
We can test for the symmetric, long-run cointegration relationship by using two bounds tests. First, following Banerjee et al. (1998), the test is named t BDM , and the null hypothesis is H 0 : 1 = 0 . If 1 = 0 , Eq. (3) is reduced to a regression involving only first differences, as there are no long-run relationships between these variables. Second, as suggested by Pesaran and Shin (1998) and Pesaran et al. (2001), a modified F-test, denoted by F PSS , can be applied to investigate the cointegration relationships. The joint null hypothesis is that coefficients of the level variables are jointly equal to zero ( H 0 : 1 = 2 = 3 = 4 = 5 = 6 = 0 ). If the null hypothesis is rejected, it implies that there are cointegration relationships among these variables. Similar test procedures can also be applied to test the cointegration in Eq. (4). Pesaran et al. (2001) established the upper and lower bounds for tests of t BDM and F PSS , respectively, to judge the existence of the cointegration relationship. When the calculated statistics of t BDM and F PSS exceed their respective upper critical values, there is evidence of a cointegration relationship among these variables. Conversely, if the calculated statistics t BDM and F PSS are below their respective lower critical values, it is not possible to reject the null hypothesis claiming no cointegration relationship. However, no clear conclusion can be drawn if the statistics lay between the upper and lower bounds.

Asymmetry relationship in the nonlinear ARDL framework
In Eqs. (3) and (4), we assume that the RMB exchange rate and global commodity prices have symmetric effects on China's stock prices; however, they may also have asymmetric effects (Chortareas et al. 2011;Groenewold and Paterson 2013;Roubaud and Arouri 2018). Therefore, we relax the strict restriction of symmetry and apply the asymmetric NARDL model developed by Shin et al. (2014). Following Shin et al. (2014), the NARDL model employs positive and negative partial sum decompositions to investigate the asymmetric relationship in both the short and long run. Furthermore, we obtain the partial sum processes of positive changes ( neer + t ) and negative changes ( neer − t ) by decomposing neer t as neer t = neer 0 + neer + t + neer − t : where neer + t and neer − t are partial sum processes of positive and negative changes in neer t , respectively. Then, we introduce neer + t and neer − t into the symmetric ARDL-ECM model (3), which can then be developed into the NARDL-ECM model, as follows: where − + 2 / 1 , − − 2 / 1 , − 3 / 1 , − 4 / 1 ,− 5 / 1 and − 6 / 1 are the long-run influence coefficients ofneer + ,neer − , fr,i,ipi , and m2 on China's stock prices. In particular, − + 2 / 1 and − − 2 / 1 denote the long-run influence coefficients of the RMB exchange rate's appreciation and depreciation on China's stock prices, respectively.
Similarly, two bounds tests are proposed to investigate the existence of a long-run cointegration relationship in the NARDL. The first is the t BDM test, which is similar to the ARDL suggested by Pesaran et al. (2001). The null hypothesis is H 0 : 1 = 0 . If the null hypothesis cannot be rejected, Eq. (5) reduces to the linear regression involving only first differences, implying that there is no long-run cointegration relationship among the levels of sp , neer + , neer − , fr , i , ipi and m2 . The second is referred to as the F pss test, a joint null of the modified F-test to investigate the long-run cointegration relationships among variables. The joint null hypothesis is H 0 : 1 = + 2 = − 2 = 3 = 4 = 5 = 6 = 0. Once the long-run cointegration relationship is identified in Eq. (5), we can obtain the long-run influence coefficients of the RMB exchange rate rising and falling to China's stock prices, which can be expressed as β neer + = − + 2 / 1 and β neer − = − − 2 / 1 , To test the long-run symmetry, we use the Wald test, with the null hypothesis being H 0 : β neer + = β neer − . If the long-run symmetry hypothesis is not rejected, we can infer that the effects of exchange rate appreciation and depreciation on stock prices are the same in the long run. Thus, Eq. (5) can be simplified as: We can then check the short-run asymmetric relationship by the null hypothesis in two ways: (1) H 0 : δ + 1,j = δ − 1,j , for all j = 0, 1, ..., n2 , or (2) H 0 : n2 j=0 δ + 1,j = n2 j=0 δ − 1,j , j = 0, 1, ..., n2 . In the short run, stock prices adjust differently to an appreciation than a depreciation if the sum of each of the dynamic coefficients associated with ' + ' differs from that associated with '−' . If the short-run symmetry hypothesis cannot be rejected, Eq. (5) can be simplified to Eq. (7), which represents an asymmetric longrun relationship only and yields the following: Similarly, we can also obtain the partial sum processes of the positive changes ( comm + t ) and negative changes ( comm − t ) by decomposing comm t as comm t = comm 0 + comm + t + comm − t : where comm + t and comm − t are partial sum processes of positive and negative changes in comm t . Then, we introduce neer + , neer − , comm + , and comm − into the symmetric ARDL-ECM model (4) and get the NARDL-ECM model, presented as follows: Similarly, we can obtain only the short-run asymmetric NARDL model (Eq. (9)) or only the long-run asymmetric NARDL model (Eq. (10)), concerning global commodity prices, using the short-run (long-run) asymmetric Wald test, as above. 3

Data description
In our empirical analysis, we use monthly data from July 2005 to December 2020 of China. Because China began to adopt a managed floating exchange rate regime since July 2005, and the RMB exchange rate fluctuations became more resilient, December (9) (1) The test equation includes both trend and intercept, and the optimal lags are determined using the Schwarz information criterion. The maximum lags are 8. (2) The p-values of the ADF and PP tests adopt MacKinnon's (1996) one-sided p-values.
(3) ***, ** and * denote significance at the 1%, 5% and 10% levels, respectively. (3) Table 2 Symmetric and asymmetric estimation results for exchange rates pass through to stock prices (1)***, ** and * denote significance at the 1%, 5%, and 10% levels, respectively; (2) maximum lag lengths of n k and l k are 6, and the general-to-specific approach is used to decide the final specifications by dropping all insignificant variables; (3) β neer indicates the symmetric long-run coefficient of the nominal effective exchange rates to the stock prices; (5)   To avoid the spurious regression problem, we adopted the augmented Dickey-Fuller (ADF) test and the Philips-Perron (PP) test to investigate the integration of the variables before the regression. As shown in Table 1, the series are either I(0) or I(1), which conform to the stationarity requirements of the ARDL and NARDL models (Shin et al. 2014). 4 Following Pesaran et al. (2001) and Shin et al. (2014), we can use all variables in level for regressions in the ARDL or NARDL models.

The impact of the RMB exchange rate on China's stock prices
Our empirical analysis is divided into two parts. First, we examine the symmetric effects of the RMB exchange rate on China's stock prices, as expressed in Eq. (3), using the ARDL model. We also analyze the asymmetric impact of the RMB exchange rate on China's stock prices, as described in Eqs. (5), (6), or (7), using the NARDL model, as determined by the aforementioned Wald test. Table 2 shows the symmetric and asymmetric effects of the RMB exchange rate on the Shanghai Composite Index (left side of Table 2) and the symmetric and asymmetric impact of the RMB exchange rate on the Shenzhen Composite Index (right side of Table 2).
On the left side of Table 2, it can be seen that, whether in the ARDL or NARDL model, both F PSS and t BDM tests are unable to reject the null hypothesis of no cointegration relationship at a 5% significance level. Moreover, the long-run coefficient of the exchange rate β neer is not significant at the 10% significance level either. The results indicate no long-run cointegration relationship between the RMB exchange rate and the Shanghai Composite Index. The impact of the RMB exchange rate on China's stock prices is also not significant. To ensure the robustness of the estimation results, we further examine   the symmetric and asymmetric effects of the RMB exchange rate on the Shenzhen Composite Index. Consistent with the above results, in both the ARDL and NARDL models, no long-run cointegration relationship is confirmed between the RMB exchange rate and China's stock prices. Hence, China's stock prices are not sensitive to fluctuations in the RMB exchange rate.

The impact of the RMB exchange rate and global commodity prices on China's stock prices
As discussed, global commodity prices can ultimately impact the stock market by affecting the listed enterprise input costs and profits and changing investor expectations for stock prices. China is a major importer of commodities. With the deepening of the exchange rate system reforms and the expansion of the RMB exchange rate's floating range, China's stock market may be more vulnerable to fluctuations in global commodity prices. Therefore, one plausible explanation for the unidentified relationship between the RMB exchange rate and China's stock prices is the omission of the critical global commodity prices variable. To verify our conjecture, we introduce global commodity prices into the ARDL, as expressed in Eq. (4), and obtain the NARDL model. This is done to further detect the symmetric and asymmetric influences of the RMB exchange rate and global commodity prices on China's stock prices. Applying the short-and longrun Wald test for symmetry, the ultimate models are shown in Table 3. Notes: (1)***, ** and * denote significance at the 1%, 5%, and 10% levels, respectively; (2) maximum lag lengths of n k and l k are 6, and the general-to-specific approach is used to decide the final specifications by dropping all insignificant variables; (3) β neer and β comm indicate the symmetric long-run coefficients of the exchangerates and global commodity prices on China's stock prices; β comm + and β comm − refer to the rising and falling long-run coefficients of global commodity prices on China's stock prices; (5)F PSS indicates the Paseran-Shin-Smith F test statistic (2001), and following Shin et al. (2014), the conservative of critical values is adopted, k = 6, and the upper bound test statistics at 10%, 5% and 1% are 3.23, 3.61 and 4.43, respectively; the upper bound of t BDM test statistics at 10%, 5%, and 1% are − 4.04, − 4.38 and− 4.99, respectively; (6)χ 2 norm , χ 2 sc , χ 2 HET , and χ 2 Ramsey denote the test of Normality, the Breusch-Godfrey LM test for serial autocorrelation, the Breusch-Pagan test for heteroskedasticity, and the Ramsey RESET test, respectively; (7)W LR refers to the Wald test for longrun symmetry, the relevant joint null hypotheses are − + 2 / 1 = − − 2 / 1 and − + 3 / 1 = − − 3 / 1 respectively, while W SR refers to the Wald test of short-run symmetry and the relevant joint null hypotheses are I2 j=0 δ + 2,j = I2 j=0 δ − 2,j and I2 j=0 τ + 2,j = I2 j=0 τ − 2,j respectively; (8) standard error and p-values are displayed in parentheses and brackets, respectively; (9) Cusum denotes the CUSUM and CUSUM squared test for stability of parameters In the ARDL model, the t BDM test is not statistically significant at the 5% level, which confirms that no cointegration exists among the RMB exchange rate, global commodity prices, and the Shanghai Composite Index. 5 In other words, if asymmetry is not considered, there would seemingly be no long-run cointegration relationship among the RMB exchange rate, global commodity prices, and the Shanghai Composite Index, as before. Moreover, the influence coefficient of the RMB exchange rate on stock prices is similarly not significant at 5%.
On the other hand, when we verify the asymmetric relationship among the RMB exchange rate, global commodity prices, and China's stock prices with the NARDL model, both the F pss and t BDM tests are statistically significant at the 5% level. This statistic confirms a long-run cointegration relationship among the RMB exchange rate, global commodity prices, and the Shanghai Composite Index. Moreover, the long-run coefficients β neer , β comm + , and β comm − are all statistically significant at the 1% level. This denotes that China's stock prices respond considerably to changes in the RMB exchange rate and respond to the rise and fall of global commodity prices with varying degrees. On the left of Table 3, we can see a negative correlation between the RMB exchange rate and the Shanghai Composite Index. According to the Wald test, there is no asymmetric effect of the RMB's effective exchange rate on the Shanghai Composite Index both in the long and short run.
Nevertheless, there is an asymmetric impact of global commodity prices on the Shanghai Composite Index in the long run, and the W LR,comm is statistically significant at the 5% level. This demonstrates that the asymmetric impact of global commodity prices on the Shanghai Composite Index is remarkable in the long run. Specifically, the positive ( β comm + ) and negative ( β comm − ) long-run impact coefficients of global commodity prices on China's stock prices are -3.386 and -1.815, respectively, and both are statistically significant at the 1% level. The absolute value of the negative long-run impact coefficient of global commodity prices is much smaller than the positive one, indicating that China's stock prices are more sensitive to positive changes than negative movements in global commodity prices. In other words, the decline in China's stock prices caused by the rise in global commodity prices is greater than the increase in China's stock prices caused by the decline in global commodity prices.
Moreover, when the critical variable of global commodity prices is added in the NARDL model, the adjusted R-square of the model is bigger than other models, which indicates that the model's explanatory power is enhanced. When considering global commodity prices in the NARDL model, the regression results perform better based on the cointegrations, significances of coefficients, and adjusted R-square, when comparing the outcomes in Table 3 with Table 2.
In diagnostic test statistics, the Breusch-Godfrey LM test (χ 2 sc ) and the Breusch-Pagan test ( χ 2 HET ) show no serial autocorrelation and heteroskedasticity in the residual. The CUSUM test (Cusum) and the Ramsey RESET test ( χ 2 Ramsey ) indicate that the estimated parameters are stable, and the NARDL model set is appropriate.
Considering the actual state of China's stock markets, and to ensure the robustness and effectiveness of the empirical results, the Shenzhen Composite Index is used as a proxy for China's stock prices too. We revisit the empirical study above, and the results are shown on the right side of Table 3. It can be seen that the results are consistent with the conclusions from the left side of Table 3, where the Shanghai Composite Index is chosen as the proxy for China's stock prices, indicating that our outcomes and conclusions are robust.
Specifically, in the symmetric ARDL model, the F pss and t BDM tests are not statistically significant at the 5% level. Thus, if asymmetry is not considered, it also shows no longrun cointegration relationship among the RMB exchange rate, global commodity prices, and the Shenzhen Composite Index.
However, if we adopt the NARDL model to investigate the effects of the RMB exchange rate and global commodity prices on the Shenzhen Composite Index, then both the F pss and t BDM tests are statistically significant at the 1% level. The long-run cointegration relations among these underlying variables are substantial, which further indicates that it is necessary to consider the asymmetric effects of exchange rates and global commodity prices on stock prices in China.
In the NARDL model, the long-run influence coefficient of the RMB exchange rate on the Shenzhen Composite Index ( β neer ) is -5.104; this result indicates that a rise (decrease) in the RMB exchange rate causes the Shenzhen Composite Index to decline (increase). The Wald test demonstrates no asymmetric effect of the RMB exchange rate on the Shenzhen Composite Index in the long run. Nevertheless, the impact of global commodity prices on the Shenzhen Composite Index is significant and asymmetric in the long run because the W LR,comm test is statistically significant at the 5% level. Moreover, the positive ( β comm + ) and negative ( β comm − ) long-run coefficients of global commodity prices on the Shenzhen Composite Index are -3.755 and -2.168, respectively, both at a statistically significant level of 1%. This indicates that changes in global commodity prices have an asymmetric impact on the Shenzhen Composite Index as well. Additionally, the rise effect on the Shenzhen Composite Index, induced by the decrease in global commodity prices, is much smaller than the decline effect caused by the increase in global commodity prices. Moreover, the results of the diagnostic test statistics indicate that there are no serial autocorrelation and heteroskedasticity in the residual, that parameters estimated are stable, and that the model set is appropriate.
In general, our empirical results show that there is a long-run cointegration relationship between the RMB exchange rate and China's stock prices when global commodity prices are taken into consideration in the NARDL model, and that the RMB exchange rate has a negative effect on China's stock prices. When the RMB appreciates, China's stock prices will decline; otherwise, China's stock prices will increase. As a large emerging economy, China has insisted on its export-oriented development strategy for decades. Thus, a significant number of products exported by enterprises have become fundamental to rapid economic growth. If the RMB appreciates, the products of Chinese exporters priced in foreign currencies will become more expensive, thus weakening the global competitiveness of Chinese exports and inhibiting exports. Such a situation would lead to a decline in earnings and potential earnings of listed companies, ultimately lowering stock prices. Conversely, if the RMB depreciates, Chinese products denominated in foreign currencies will become less expensive, stimulating exports, thereby increasing enterprise earnings. When high earnings result in an increase in projected earnings, stock prices rise. Therefore, the RMB exchange rate is negatively correlated with China's stock prices.
In studying the impact of global commodity prices on stocks, we find an asymmetric relationship. China's stock prices are more sensitive to an increase in global commodity prices than a decrease. The global commodity market has long been monopolized by a small number of oligarchic companies. Simultaneously, China's industry concentration ratio is low compared with other developed economies, so it is difficult for Chinese companies to form price alliances and gain strong bargaining power in the face of commodity oligarchs. Thus, given the low concentration of industry and the dispersion of corporate power, when global commodity prices rise, oligarchs tend to raise their commodity prices sharply. Simultaneously, domestic commodity prices also significantly increase. Moreover, there is excessive competition in China's downstream product market due to an overcapacity problem. To maintain a competitive price advantage and stabilize the market share of products, downstream manufacturers or companies can only slightly raise the selling prices of their products and have to passively accept rising commodity prices. In this case, rising global commodity prices will considerably increase company production costs and drastically reduce their profitability, eventually causing stock prices to fall sharply in anticipation of reduced profitability. However, when global commodity prices fall, relying on their monopoly power in the domestic market, commodity suppliers in the Chinese market maintain relatively high domestic commodity prices. Hence, the production costs of Chinese companies only slightly decline, and in turn, their profits only slightly rise, eventually causing stock prices to increase marginally. Thus, the increase in global commodity prices drive China's stock prices to decline sharply; however, the same magnitude of decline in global commodity prices induces a smaller rise in China's stock prices.
Since the NARDL model confirms the asymmetric cointegration relationship, and the effect of global commodity prices on China's stock prices is asymmetric in the long run, we can draw the asymmetric dynamic trajectories of stock prices by unit increase and falling global commodity prices using asymmetric cumulative dynamic multipliers. The when h → ∞ , then m + comm,h → β comm + and m − comm,h → β comm − , where β comm + = − + 3 / 1 and β comm − = − − 3 / 1 are the positive and negative asymmetric longrun coefficients of global commodity prices to China's stock prices, respectively. Figure 1 shows the asymmetric trajectories of the Shanghai and Shenzhen Composite Indexes after the rise and fall of unit global commodity prices. Specifically, both indexes are more sensitive to increases than decreases in global commodity prices. Furthermore, the increase in global commodity prices causes China's stock prices to decline sharply, while the same magnitude of decline in global commodity prices induces a smaller increase in China's stock prices. The asymmetric dynamic multiplier results further support our previous findings that the impact of commodity prices on stock prices is indeed asymmetric in the long run.

Conclusion
This study investigates both the symmetric and asymmetric impact of the RMB exchange rate on China's stock prices using the ARDL and NARDL models. However, all the results indicate that there is no cointegration relationship when the key variable-global commodity prices-is absent. After the inclusion of global commodity prices, the empirical results reveal a long-run cointegration relationship among the RMB exchange rate, global commodity prices, and China's stock prices in the NARDL model. The changes in the RMB exchange rate have a negative effect on China's stock prices. As a large emerging economy, China has long insisted on an export-oriented economic development strategy. Thus, with the rapid expansion of the RMB exchange rate's floating range, fluctuations in the RMB exchange rate will eventually influence China's stock market by affecting the global competitiveness of the listed companies' exports.
We also find that the impact of global commodity prices on China's stock prices is asymmetric, and that China's stock prices are more sensitive to increases than to decreases in global commodity prices. In other words, the rise in global commodity prices causes China's stock prices to decline sharply, while the same magnitude of decline induces a smaller increase in stock prices. Chinese companies have lacked pricing power in global and domestic commodity markets for a long time; thus, Chinese companies are forced to bear high production costs when global commodity prices increase. This results in a sharp reduction in current and expected corporate profits and eventually a significant decline in China's stock prices. When global commodity prices fall, relying on monopoly and higher bargaining power, the commodity monopolists refuse to cut prices significantly. As a result, the production costs of downstream enterprises only decreases minimally, while China's stock prices only slightly rises. Therefore, with the rapid expansion of the RMB exchange rate's floating range, the exchange rate exposure faced by the Chinese stock market and enterprises has (11) m + comm,h = h j=0 ∂sp t+j ∂comm + t , and m − comm,h = h j=0 ∂sp t+j ∂comm − t . h = 0, 1, 2 . . . , expanded. The government must accelerate RMB globalization and improve its status in global trade. Considering the asymmetric impact of rising and falling global commodity prices on China's stock prices, authorities should adopt asymmetric and precise regulations to achieve the goal of stabilizing the stock market. Meanwhile, China should actively bid for overseas resources, break the monopoly pattern of the global commodity market, and strive for pricing power in global commodities. In addition, China is slated to accelerate improvement of the country's commodity futures markets and create conditions for Chinese companies to use hedging instruments, such as futures and options, to enhance their ability to resist risks and maintain financial stability.