The Nonlinear Dynamic Relationship between Stock Prices and Exchange Rates in Asian Countries

This study explores dynamic relationships between stock prices and exchange rates in Asian countries. These relationships are complex and include both linear and nonlinear relationships. We employ a nonparametric causality test to explore them. The nonparametric causality test is more robust to a nonlinear relationship. The empirical results reveal that most countries have bi-directional causality relationships between stock prices and exchange rates. Some relationships are not captured by the linear model. These results support the theoretical model which shows dynamic interactions between stock and exchange rate markets. This study investigates the main driver to generate the nonlinear causality relationships. The empirical results present that the main source for the nonlinearity is the volatility effects. In particular, they were substantial during the Asian and global financial crises. After controlling for the volatility effects, only one country shows the bi-directional causality relationship. In contrast to the previous studies, this study shows that the volatility effects are important between different asset markets. These findings suggest that controlling for exchange rate markets may be helpful to mitigate turmoil during a financial crisis.


Introduction
The linkage between stock prices and exchange rates has been of interest to researchers for a long time. Two important theories that explain this relation are the flow-oriented model and the stock-oriented model. (Note 1) The flow-oriented model was first suggested by Dornbusch and Fischer (1980); since exchange rates alter a firm's international competitiveness, their model demonstrates that the movement of exchange rates impacts stock prices. In contrast, Branson (1983) and Frankel (1983) proposed the stock-oriented model. They describe the manner in which stock prices affect exchange rates in the following way: when the domestic country's stock prices increase, domestic consumption also increases, and this increases the domestic investors' demand for money. Therefore, the domestic interest rate becomes higher than the interest rates of other countries.
Empirical studies have found links between stock prices and exchange rates in developed countries. Ma and Kao (1990) use monthly data from six developed countries and found that the export-dominant countries had negative relations with currency appreciation. Ajayi and Mougoue (1996) report that an increase in domestic stock prices negatively impacted exchange rates in the short term and positively impacted exchange rates in the long term. Chow, Lee, & Solt (1997) demonstrate that real exchange rates and stock returns were positively correlated in the long term in the U.S., while Nieh and Lee (2001) conclude that only short-run relationships exist between stock prices and exchange rates in the G7 countries. Recently, Phylaktis and Ravazzolo (2005) focus on Asian counties and show that there are long-run relationships among their stock prices, real exchange rate, and U.S. stock price. Causality tests are employed by Granger, Huang, & Yang (2000) and Pan, Fok, & Liu (2007) to examine the Asian financial crisis period.
In this study, we investigate the dynamic relationships between stock prices and exchange rates in Asian countries. Exploring Asian countries is important since they have had two crises in our sample period, which were the Asian financial crisis in 1997 and the global financial crisis in 2008. These crises, however, have several differences. For instance, Erb, Harvey, & Viskanta (1998) and Ito (2007) point out that the Asian financial crisis was a currency crisis. Since this crisis, some Asian countries have accumulated international reserves to avoid a future currency crisis, as shown by Aizenman and Marion (2003) and Aizenman and Lee (2008). In contrast, the global financial crisis was led by complex financial instruments and financial markets were more integrated as pointed out by Claessens, Kose & Terrones (2010). Lin (2012) addresses that after the global financial crisis, new money inflows to Asian countries occurred by quantitative easing policies conducted by the U.S., U.K., and Euro-zone.
Recent theoretical and simulation studies imply that the relationships between stock prices and exchange rates are complex. For instance, Dieci and Westerhoff (2010) propose a theoretical model which generates a dynamic relationship between stock markets and an exchange rate market. Their model has traders who trade based on fundamental information in the stock markets and heterogeneous traders in the exchange rate market, which contains both fundamental and technical traders. Corona, Ecca, Marchesi, & Setzu (2008) examine the interactions between stock and exchange rate markets using an artificial market. They present that there are dynamic interactions even without any external news. Taken these theoretical and computer simulation models, the nonparametric approach which can capture both linear and nonlinear causality relationships is promising.
To this end, we use the nonparametric Granger causality test proposed by Diks and Panchenko (2006) (henceforth DP) is applied in this study. This method extends the studies of Baek and Brock (1992) and Hiemstra and Jones (1994) and is widely applied in several fields; exchange rate markets (Bekiros and Diks 2008a), energy markets (Bekiros and Diks 2008b), interest rates (Ajayi and Serletis 2009), and market sentiment (Dergiades 2012). This study differs from Yang, Tu, & Zeng (2014), because our approach explores impacts of the volatility effects. The causality relationships might come from the conditional variance, as pointed out by Hiemstra and Jones (1994), and Bekiros and Diks (2008a). This study also takes into account a long-run relationship, since Bekiros and Diks (2008b) highlight that the co-integration relationship might affect the nonlinear causality result.
This study finds that the nonparametric method is successful in capturing the causal relationships which are not captured by the conventional method. We reveal that most Asian countries have bi-directional causality relationships between stock prices and exchange rates. More importantly, we present that the main driver for the nonlinear relationships is the volatility effects. All countries, except Singapore, lose the bi-directional causality relationships after controlling for the volatility effects. This paper is organized as follows: Section 2 explains the methodologies; Section 3 describes the data; Section 4 reports the empirical results; Section 5 conducts further research; and Section 6 concludes the study.

Testing Stationarity
The DP nonparametric test requires stationary data series. For a stationary test, we employ the Modified Dickey and Fuller (DF-GLS) test proposed by Elliott, Rothenberg, & Stock (1996). This test extends the Dickey and Fuller (1979) test and if the data series have a deterministic mean or trend, the asymptotic power of DF-GLS is greater than the conventional Augmented Dickey and Fuller (ADF) test. The test statistic is obtained as: (1) where ̂ . contains a constant term and does not include a trend term in this study. The null hypothesis is =0 and if there is no trend term, the Dickey-Fuller t statistic is applied for a statistical inference as in Elliott et al. (1996). The number of lags in equation (1) is determined by the Bayesian information criterion (BIC).

Cointegration Test
We use the Johansen cointegration approach proposed by Johansen (1988) to investigate a long-run relationship between stock prices and exchange rates. We consider the following reduced form error correction model (ECM): is a matrix of short run adjustment parameters, is a matrix of cointegration vectors, and is the error term. The Johansen trace test statistic is employed in this study. The number of lags in equation (2) is determined by the BIC. The null hypothesis is that there are at most cointegration vectors and the trace statistic is: where ̂ is the smallest squared canonical correlations of corrected for lagged differences and is the sample size. There are five specifications of equation (2) as in Johansen (1995). Although we use the Pantula principle to determine deterministic components of the model as in Nieh and Lee (2001), Hjelm and Johansson (2005) propose to exclude the no deterministic components model, since the model is too restrictive. The Pantula principle suggests the restricted constant model for all data.

Nonparametric Granger Causality Test
This subsection explains the DP nonparametric Granger causality test. First, it describes a conventional Granger causality test. The Granger (1969) Finally, the test statistic is estimated as: where ̂ is the local density estimator of a -variate random vector W at , and ̂ is denoted by an indicator function as follows:  (7) is asymptotically distributed as Following DP, the bandwidth is set as: . This DP causality test is applied into residuals of a vector autoregression (VAR) model. Following to Pan et al. (2007) and Lin (2012), this study considers the following VAR model and controls for the interest spreads and stock returns in the Asian markets as follows: denotes the log difference of stock prices, denotes the log difference of exchange rates, and denotes the interest difference between the local interest rate and the U.S. interest rate. The local and U.S. interest rates are three-month deposit rates or three-month interbank rates.
denotes the returns on an Asian stock index (MSCI All Country Asia excluding Japan), and is computed on the local currency. and are residuals of the VAR. The number of lags of the VAR model is determined by the BIC.
When the stock price and the exchange rate are cointegrated, the error correction term is included in equations (9) and (10) as in Pan et al. (2007) and Bekiros and Diks (2008b). Since Granger (1988) and Bekiros and Diks (2008b) suggest that excluding the error correction term may cause a false causality result when there is a cointegration relationship.

EGARCH Filter
The nonparametric test can capture a nonlinear relationship and some portions of nonlinearity may be explained by the autoregressive conditional heteroscedasticity (ARCH) model as in Hsieh (1991). Nonparametric Granger causality tests are examined in terms of whether their results come from the volatility effects. Hiemstra and Jones (1994) and DP (2006) employ the Exponential -GARCH (EGARCH) model proposed by Nelson (1991) to capture the process of the conditional variance. This study also adopts the EGARCH model, since it can capture an asymmetric response of the variance as pointed out by Hsieh (1991). The conditional variance of is modeled by EGARCH (1, 1) as: where is the residuals of the VAR model in (9) and (10), and is the parameters of EGARCH. The asymmetric ARCH effect can be captured by and For the estimation, the EGARCH (1, 1) model is adopted, rather than using the BIC to determine the number of lags. Brooks (1996) proposes to use a compact representation model for the filtering. In addition, if higher lags are employed, most parameters become insignificant in this study.

Data
This section explains the data series. This study uses daily closing foreign exchange rates denoted relative to the U.S. dollar (USD) and daily closing stock price indices for eight Asian countries. All data are obtained from the Thomson Reuters Datastream. (Note 3) Although data frequencies are important as in Huang and Jo (1995), and Narayan and Sharma (2015), this study focuses on daily frequency. The nonparametric test requires much more observations than a conventional method and monthly and weekly frequencies are difficult to collect enough observations. Moreover, Chamberlain, Howe, and Popper. (1997) show that low frequency data may not capture exchange rate exposure compare with daily frequency data. The sample period extends from November 2, 1995 to December 30, 2013.
Eight countries have been selected in this study: Indonesia, Korea, Japan, Hong Kong, Malaysia, the Philippines, Singapore and Thailand. Since these countries have been selected for study in most of the previous studies, it is possible to compare the results. The stock indices are Jakarta Stock Exchange Composite Index (Indonesia), Kospi200 (Korea), TOPIX (Japan), the Hang Seng Index (Hong Kong), FTSE Bursa Malaysia KLCI30 (Malaysia), Philippine SE Composite Index (Philippines), FTSE Straits Times Index (Singapore) and SET index (Thailand). These indices are based on local currencies and all data are transformed into logarithmic scale.    -Lenum (1992). The number of lags is determined by the BIC. *,**, and *** indicates that the null hypothesis is rejected at the 10%, 5%, and 1% level, respectively.

Empirical Results
We move onto the main results in Table 3 providing the Granger causality results. First we focus on the linear causality test in column (1). The stock returns Granger cause the exchange rate returns in Indonesia at the 1% level and in Singapore at the 5% level. Thailand has the opposite relation and Japan, Korea, and the Philippines have bi-directional relationships. Malaysia does not have any relationships. This country has had a fixed exchange rate regime for several years, which may cause the weak relationship.
Given the linear results, we examine the nonparametric results in column (2) of Table 3. The nonparametric test can capture both linear and nonlinear relationships. All linear causality relationships remain statistically significant at least at the 5% level in column (2). Interestingly, the nonparametric test is successful in capturing additional relationships in Indonesia, Singapore, and Thailand. These indicate the advantage of applying the nonparametric method. The nonparametric results suggest that all countries except Malaysia have bi-directional relationships. These imply that the relationships between stock prices and exchange rates are dynamic and are supportive of the theoretical model of Dieci and Westerhoff (2010). It is difficult to conclude whether the stock-oriented or flow-oriented models determine the relationships.  (9) and (10). The nonparametric result is estimated by the nonparametric Granger causality test using the residuals of the VAR. EGARCH indicates the residuals of the VAR are filtered by the EGACRH model as in equations (11) and (12). Panel B uses the VEC model which adds the error correction term into the VAR. **, and *** indicate that the null hypothesis is rejected at the 5% and 1% level, respectively.
The next test assesses whether the volatility effects impact the nonparametric causality test. Hsieg (1991) highlights that the volatility effects cause nonlinearities in stock returns and Brook (1996) finds the same results in exchange rate markets. We conduct the nonparametric causality test after filtering the residuals of equations (9) and (10) using the EGACRCH model. Column (3) in Table 3 provides evidence that more than half of the causality relationships become insignificant after the EGARCH filtering. All countries, except Singapore, do not have the bi-directional relationships.
Theses imply that conditional volatility is a main determinant of the nonlinear causality relationships. In contrast to the previsus studies, we find that the volatility effects are important between the different asset markets.
Finally, we focus on columns (4) and (5) which are estimated using the residuals of the vector error correction (VEC) model, since Table 2 suggests that there is a long-run relationship in Hong Kong. We can see the nonparametric test in column (5) captures the feedback relationships not revealed by the conventional model in column (4). In summary, all countries except Malaysia have bi-directional causality relationships for the entire sample period.
Given the cointegration test results, we move onto the causality test. We employ the log first difference data and do not include the error correction term. Table 5 shows the results of the causality test. Columns (1) and (2) show that the nonparametric test captures the relationships which are not captured by the linear causality test. Indonesia, Korea, Malaysia, and the Philippines have bi-directional relationships during the Asian crisis and the exchange rate returns Granger cause the stock price returns in Japan, Singapore, and Thailand. These results imply that the Asian crisis affects the exchange rate markets and consistent with the view of Erb et al. (1998) and Ito (2007). Surprisingly, after the EGARCH filter, only two relationships remain statistically significant in column (3). The volatility effects have greater impacts on the causality relationships during the Asian crisis.
Indonesia, Japan and Korea have feedback relationships between exchange rate returns and stock returns during the global crisis in column (5). In contrast, the stock returns Granger cause exchange rate returns in Malaysia and Singapore, and the opposite relation holds in Thailand. Most relationships become insignificant after the EGRACH filter and these are similar to the results during the Asian crisis. We can find that the volatility effects are substantial for the nonlinear causality relationships during both crises.

Conclusion
This study has explored the causal relationship between exchange rates and stock prices. The relationship has dynamic interaction. For instance, Dieci and Westerhoff (2010) and Corona et al. (2008) propose theoretical or simulation models to capture the dynamics. This dynamic relationship causes difficulty to explore a causal relationship using a conventional Granger causality method. To capture the dynamic relationship, we employ the nonparametric Granger causality test proposed by Diks and Panchenko (2006). This approach is more robust to nonlinear relationships.
The empirical results reveal that the nonparametric method is successful in capturing the causality relationships which are not captured by the linear causality test. Most countries have feedback relationships between stock and exchange rates. The volatility effects are strongly linked to the nonlinear causality relationships. In particular, the volatility effects play substantial roles during the financial crises. These findings suggest that economic policy to reduce volatility in the exchange rate such as a pegged exchange rate system may be helpful to mitigate the dynamic relationships during a crisis.