Empirical Testing of Co-integration of International Financial Markets with Reference to India,the USA,Japan,and Hong Kong

Abstract

This article examines the co-integration among the financial markets of four countries (India, the USA, Japan, and Hong Kong) from April 2010 to May 2021. Using the Johansen co-integration test, we establish the integration between the stock markets of these countries. The test clearly shows that there exists long-run co-integration between these countries. Furthermore, we checked the relationship of one country with another by applying the multivariate Granger causality test, which shows the influence of the US market over the other countries. The results significantly show the existence of long-run co-integration and linkages between these financial markets. Applying the Vector error correction model and variance decomposition analysis for the period confirms the result obtained from multivariate Granger causality. As the study shows, the stock market of the countries is not entirely inter-linked. However, some tests provide the pairwise linkages but not when talking about all the nations together. That means the rise in one stock market does not necessarily impact the surge in other stock exchanges, which means investors can profit from diversifying between these stock exchanges. It provides the opportunity for portfolio diversification to investors. The study shows that “the international stock market is neither fully integrated nor completely segmented,” giving international diversification an opportunity. As in our study, the “U.S. market is the most exogenous,” and the Japanese market is relatively isolated from the other market, where the impact from the different markets is not that significant.

Keywords

International stock market co-integration analysis integration and segmentation of world market vector error correction model variance decomposition analysis impulse response function

Introduction

The integration of international financial markets has been perceived to be a very significant and crucial factor for any country’s financial market since the present era is a period of globalization and every single country in the world is dependent on one another for their performance (Wang et al., 2013). In the stock market, the integration of the financial market among the countries affects the firms listed on the exchanges. Suppose the investors have an opportunity to invest in an entirely foreign market portfolio, investors can frictionlessly trade each asset class across the markets. In that case, financial markets are all fully integrated. All investors will expose to the common risk factor in the same way (Greenwood et al., 2018). They affect the asset prices in the foreign market, so an investment barrier exists, and the foreign market is not fully integrated (Patro, 2001). The linkages between the international financial markets provide substantial relief to the investors in the form of lower cost of capital (El Hedi Arouri et al., 2013) and the allocative efficiency of their capital. Still, it also imposes particular challenges in their legal, institutional, and cultural environment, which create difficulties quantifying the degree of integration and its impact on one financial market to another (Pirinsky & Wang, 2011). Market segmentation is yet another strong phenomenon of the market situation defined as a condition in which identical securities are not identically priced in the markets (Thomadakis & Usmen, 1991).

The theory supports the widely accepted notion that the world market is neither fully integrated nor completely segmented (Errunza et al., 1992). There must be a causal relationship between financial markets of countries together, depending on the condition of market structure for the country and the level of integration. With the substantial deregulation of the financial market, capital flows across the border, a considerable amount of foreign investment, and foreign portfolios in consideration of the world of financial markets may be expected to move together up to some extent. Furthermore, the market-driven movement of the stock return may be directed by the degree of integration of the market structure. Hence, the extent of international financial market linkages is an essential matter of testing.

Compared to the large body of literature on international financial bond linkages (e.g., Barassi et al., 2001; Smith, 2002; Yang, 2005) and international money market linkages (e.g., Fung & Isberg, 1992), only a few empirical works have examined the linkages between international financial markets with the consideration of the Indian stock market. Applying a co-integration technique did not find any co-integration between the six markets and confirms that each of the six markets is not linked with other markets in the long run (Yang, 2003), and Eun and Shim (1989) confirm that no single market can significantly explain the movement in the US market. By contrast, Schöllhammer and Sand (2018) and Jaffe and Westerfield (1985) reported the substantial interdependence and existence of co-integration among the stock market. Gulzar et al. (2019) found that there exists a long-term co-integration between the US market and emerging stock markets (Agoraki et al., 2019). It is evident from the empirical findings that whether the market is co-integrated or not is entirely inconclusive and represents the number of different perspectives, thus calling for a more thorough analysis.

This article more comprehensively examines the stock market linkages including the long-run co-integration relationship between market return and linkages between the movements of various stock markets across the world. The study contributes to the literature in several aspects: first, to examine the controversy over the non(existence) of the international financial market, the stability of the long-run relationship is investigated by applying the recursive co-integration technique to test whether the co-integration relationship occurs during the sample period; Second, the most important purpose of the article is to check the relationship between these stock markets and to check the impact of one stock market on another by checking the casual pattern of strong correlations between the markets and is explored based on the multivariate Granger causality test (Bessler & Yang, 2003; Yang, 2003, 2005). In addition, this study examines the linkages between the stock prices in major world stock exchanges, such as India, Hong Kong, Japan, and the USA, using daily closing data from January 2010 to May 2021. After that, we investigate the impact of stock market movement in one market over the other.

Data

The data for this study include daily adjusted closing price data of four significant indexes from the different countries, covering a long period from April 2010 to May 2021. The four major stock markets under study are as follows: Nifty 50 (India), Nasdaq (USA), Nikkei 225(Japan), and Hang Seng (Hong Kong). The sample consists of 2,780 observations after adjusting the national and bank holidays. The previous studies (Arshanapalli & Doukas, 1993; Bessler & Yang, 2003; Yang, 2003) also used daily adjusted closing prices and focused on the USA, Japan, and Hong Kong countries for their importance in the international financial market. India is selected from the view of seeing the response of the Indian stock market with the movement of the global market. The data employed in the study are collected from the website of Yahoo finance. The graph presents the closing price of four indices from April 2010 to May 2021, indicating that these four indices move in the same direction and depict a clear trend over the period.

Methodology

The methodology of this study involves various steps as follows:

Determine the presence of the unit root in each of the indices involved. This basically involved the augmented Dickey–Fuller (ADF) unit root analysis.

The next step involves estimating the co-integration equation, where all the financial markets are being tested for integration.

The next step is selecting optimum lag length with the help of Akaike’s information criteria, Schwarz criteria, and Hannah Quin criteria. With the help of these criteria, the optimum lag is selected.

The final step involves applying a multivariate Granger causality test for checking the impact of one stock market over the other.

Econometric Methodology

The present study is based on the vector auto regression (VAR.) framework. The co-integration test in the study follows the procedure of Johansen (1991). Let X_t denote a vector that includes the stock index price series of four countries’ stock markets (p = 4), and the error correction model is represented as follows:

Δ X_{t} = Π X_{t - 1} + \sum_{i - 1}^{k - 1} Γ_{i} Δ X_{t - i} + μ + e_{t} (t = 1, \dots T)

(1)

The VAR. model in the first difference is presented in Equation (1), except for the lagged level of X_t₋₁. The parameter matrix, Π, contains information for long-run co-integrated information among the p variables.

In the situations where stock markets seem to be nonstationary, we can check the inter-national stock market linkage in the long run by determining the number of co-integrating vectors, r, as follows:

H (r) : Π = α β^{'}

(2)

A trace test (Johansen, 1991) is conducted to determine r. The null hypothesis for the trace test is that there are at most r (0 ≤ r ≤ p) co-integrating vectors.

The equation for the trace test is given by,

T r a c e (r, k) = - T Σ^{k} \ln (1 - λ_{i}), I = r p 1

(3)

To address the existence of co-integration in the financial market, the recursive co-integration technique helped in checking the stability of the co-integration relationship over each data point during the sample period.

In the case of co-integration (which is applicable in this study), an error correction model should be employed and estimated, which is used to summarize the dynamic influence of each market on the other and show how the one market responds to the other in terms of VAR mechanism. However, the adjustments from dynamic shocks and strength from one market to another remain unexplained because the co-efficients of the VAR model are hard to interpret. Still, we conducted the forecast error variance decomposition to summarize the linkages among the four countries’ financial markets.

Empirical Results

Unit Root Tests

Before testing for co-integration, the stationarity of stock exchanges in the same order needs to be determined. The ADF test for the unit root is performed. The test’s null hypothesis is that the national stock indices have a unit root against the alternative that they do not have. The reported result from Table 1 indicates the presence of the unit root in all indices as we failed to reject the null hypothesis. However, Table 2 suggests that there is no unit root present in these stock indices as the null hypothesis of a unit root in the first difference is rejected for all four stock index series.

The ADF test is based on the following regression:

D x_{t} = a_{0} + a_{1} x_{t - 1} + {\sum^{​}}_{m}^{j = 1} b_{j} D x_{t - j} + v_{t},

where, x_t denotes the stock market index, and v_t is an error term.

For the ADF test (in level and differences), the number in parentheses denoted the minimum value of m required to achieve white noise errors, v_t.

Co-integration Test

In this study, we then examined whether the national stock market index series are co-integrated. For checking the co-integration, we applied the Johansen co-integration test. Selection of optimum lag is a necessary step for applying the co-integration test. For the selection of optimum lag, which is required for running the co-integration test, we have conducted the VAR model, and by checking the lag structure with the lag exclusion test and Wald test, we have selected the lag of 2, which Schwarz information criteria suggest. As a result, the null hypothesis “no co-integration between stock market indices” is rejected. For this, the trace test and maximum eigenvalue test are being conducted. The result of both the tests at a 5% significance level indicates co-integration between the series. The trace test and eigenvalue test show one co-integrating equation(s) at the 0.05 level.

Table 1.

Augmented Dickey–Fuller Unit Root Test Statistics in Stock Exchange Indices: April 2010–May 2021 (level)

Country	Exchange Index	t-Statistics	p-Value
India	Nifty 50	−0.183723	0.9381
USA.	Nasdaq	1.968414	0.9999
Japan	Nikkei 225	−0.591848	0.8700
Hong Kong	Hang Seng	−2.179429	0.2140

Source: The authors.

Table 2.

Augmented Dickey–Fuller Unit Root Test Statistics in Stock Exchange Indices: April 2010–May 2021(at the 1st difference)

Country	Exchange Index	t-Statistics	p-Value
India	Nifty 50	−52.44066	0.0001
USA	Nasdaq	−55.41436	0.0001
Japan	Nikkei 225	−54.24388	0.0001
Hong Kong	Hang Seng	−53.09385	0.0001

Source: The authors.

Vector Auto Regression Lag Order Selection Criteria

Lag	LogL	LR	FPE	AIC	SC	HQ
0	6445.928	NA	1.13e-07	–4.644505	–4.635957	–4.641418
1	32170.30	51356.01	1.01e-15	–23.17974	–23.13700*	–23.16430
2	32194.44	48.12205	1.00e-15	–23.18561	–23.10867	–23.15782
3	32236.31	83.34501	9.83e-16	–23.20426	–23.09313	–23.16413
4	32272.12	71.18492	9.69e-16	–23.21854	–23.07323	–23.16606*
5	32294.77	44.95906	9.65e-16	–23.22334	–23.04383	–23.15851
6	32312.93	35.99018	9.63e-16	–23.22489	–23.01119	–23.14772
7	32335.24	44.15193	9.59e-16	–23.22944	–22.98155	–23.13992
8	32352.75	34.60127*	9.58e-16*	–23.23053*	–22.94845	–23.12866

*indicates lag order selected by the criterion

LR: sequential modified LR test statistic (each test at 5% level)

FPE: Final prediction error

AIC: Akaike information criterion

SC: Schwarz information criterion

HQ: Hannan-Quinn information criterion

VEC Lag Exclusion Wald Test

D(LN_NIKKEI)		D(LN_NASDAQ)	D(LN_NIFTY)	D(LN_HANG)	Joint
DLag 1	4.915384	4.385724	13.36179	26.04201	49.73945
	[0.2961]	[0.3563]	[0.0096]	[0.0000]	[0.0000]
DLag 2	14.39836	11.57851	33.77690	25.71845	84.49695
	[0.0061]	[0.0208]	[0.0000]	[0.0000]	[0.0000]
DLag 3	32.38898	5.808004	7.638329	28.90478	76.30600
	[0.0000]	[0.2140]	[0.1058]	[0.0000]	[0.0000]
DLag 4	8.738165	1.166709	3.940724	33.35159	76.30600
	[0.0680]	[0.8835]	[0.4141]	[0.0000]	[0.0000]
DLag 5	7.346870	0.989469	16.78317	12.52449	37.48213
	[0.1187]	[0.9114]	[0.0021]	[0.0138]	[0.0018]
DLag 6	8.854118	5.931879	20.06794	4.460848	39.75496
	[0.0649]	[0.2043]	[0.0005]	[0.3354]	[0.0008]
DLag 7	5.800298	10.72244	12.41730	3.205745	32.97938
	[0.2146]	[0.0299]	[0.0145]	[0.5240]	[0.0074]
DLag 8	3.591953	19.54479	2.552743	9.875465	35.12654
	[0.4640]	[0.0006]	[0.6352]	[0.0426]	[0.0038]
df	4	4	4	4	16

Johansen Co-integration Test

Lags interval (in first differences): 1 to 2

Unrestricted Cointegration Rank Test (Trace)

Hypothesized No. of CE(s)	Eigenvalue	Trace Statistic	0.05 Critical Value	Prob.**
None*	0.012689	62.04999	47.85613	0.0014
At most 1	0.005196	26.49798	29.79707	0.1145
At most 2	0.002881	1.99513	15.49471	0.1572
At most 3*	0.001422	3.962127	3.841464	0.0465

Trace test indicates 1 cointegrating eqn(s) at the 0.05 level

*denotes rejection of the hypothesis at the 0.05 level

**Mackinnon-Haug-Michelis (1999) p-values

Hypothesized No. of CE(s)	Eigenvalue	Max-Eigen Statistic	0.05 Critical Value	Prob.**
None*	0.012689	35.55201	27.58434	0.0039
At most 1	0.005196	14.50285	21.13162	0.3252
At most 2	0.002881	8.033005	14.26460	0.3754
At most 3*	0.001422	3.8414465	3.841465	0.0465

Max-Eigen test indicates 1 cointegrating eqn(s) at the 0.05 level

*denotes rejection of the hypothesis at the 0.05 level

**Mackinnon-Haug-Michelis(1999) p-values

Unrestricted cointegrating coefficients (normalized by b’*S11*b=I)

The application of the Granger causality test gives some very good results, which show that the US stock market affects the movement of the other three countries’ stock markets, that is, India, Japan, and Hong Kong. The Indian and Japanese stock markets affect each other, and the relationship between India and Hong Kong cannot be established. This emerges as the primary model of the study showing the relationship and effect of one market over the other.

Main Model of the Study

The null hypothesis for the Granger causality test “US market does not granger causes India, Japan and Hong Kong” is rejected as shown in Table 3 and hence it could be inferred that US market has a significant effect on financial markets of above mentioned countries. The US market has a significant impact over the other market in the long run. The Indian market is affected by US and Japanese stock markets as we have rejected the null hypothesis for US and Japanese markets. The US market is not influenced by any of the other markets as we failed to reject the null hypothesis in the case of US markets. For the Japanese market, it is clear that there is a significant effect of the US market over the Japanese market, but there is no effect on other markets. The financial market of Hong Kong is affected by the Indian market, US market, and Japanese market as, in all the three cases, the p-value is less than the 0.05 level, thus null hypothesis is rejected.

Table 3.

Multivariate Granger Causality Test

Dependent Variable	Test Statistics	Significance Level
Dependent Variable	India	USA	Japan	Hong Kong
India (Nifty)	–	5.06166 (0.0064)	7.15383 (0.0008)	1.55918 (0.2105)
USA (Nasdaq)	1.33684 (0.2628)	–	0.05073 (0.9505)	0.29350 (0.7457)
Japan (Nikkei)	3.86828 (0.0210)	3.24974 (0.0389)	–	1.05725 (0.3476)
Hong Kong (Hang Seng)	11.8222 (0.000008)	4.24281 (0.0145)	15.5779 (0.000002)	–

Source: The authors.

Note: The F-statistics are used. Numbers in parentheses are p-values.

Conclusion and Implications

The stock market relationship with each other establishes the linkages among the stock markets of India, the USA, Japan, and Hong Kong through the multivariate Granger causality test using financial data. The empirical framework is applied for investigating the interdependence of these four stock markets by combining the co-integration equation, application of the Granger causality test, and Vector error correction model in the study. Results are consistent with the recent work (e.g., Agoraki et al., 2019), the stock indexes from these four countries are co-integrated with one co-integrating vector. After that, the effect of US and Japanese markets over India and Hong Kong in the long run is shown. The US market significantly affects the other stock market including the Japanese market. The finding is aligned with the previous work of (Eun & Shim, 1989), emphasizing the prominent role of the US stock market in the world stock market. Eun and Shim (1989) in their study also support the statement that “U.S. market is the most exogenous.” As with the present era of globalization and with the increasing degree of integration between the US market and the world market, the results are not much surprising. The important point to give emphasis on is that, in the previous studies as well, it is found that the US market is probably the only market that significantly impacts the world market over the long run.

The Japanese market significantly affects the Indian and Hong Kong stock market, excluding the U.S. market, where the impact cannot be established. To our knowledge, such relationships in the integrated world equity market have not been discussed in the previous literature. This finding is consistent with the study by Bessler and Yang (2003), which shows the combined effect of the Japanese market with the US market for the responsiveness of other countries’ stock markets (Francis & Leachman, 1998). The relationship between the Hong Kong stock market and the different stock markets is checked, and it is found that the movement of the Hong Kong stock market is affected by all the three other major stock markets. The innovation in US, Indian, and Japanese markets altogether causes the modest proportion of stock price movement in this country.

The current era of globalization gives the free movement of capital across the nations giving rise to the Foreign Institutional investments. It even allows individual investors to diversify their portfolios as the markets from developed nations reach their saturation. It gives them the opportunity for new investment avenues as the stock market of the countries is not entirely inter-linked. However, some tests provide the pairwise linkages but not when talking about all the nations together. That means the rise in one stock market does not necessarily impact the surge in other stock exchanges, which means investors can profit from diversifying between these stock exchanges. In this way, they will be able to reduce their risk as well. Finally, the study shows that “the international stock market is neither fully integrated nor completely segmented,” giving international diversification an opportunity. As in our study, the Japanese market is relatively isolated from the other market, where the impact from the different markets is not that significant. While looking for the investment avenues, the investor must look beyond the influence of one stock market over the other, like macro-economic factors, which also impact the returns of these stocks. This gives the direction for future research consisting of those countries where the macro-economic factors for these countries can be studied. The study deals with the linkages between the returns from stock exchanges, volatility of the stock market, and the spill-over effect for future research.

Footnotes

Declaration of Conflicting Interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

Aditya Keshari is the awardee of ICSSR Post-Doctoral Fellowship. The paper “Empirical Testing of Co-integration of International Financial Markets with Reference to India, the USA, Japan, and Hong Kong” is largely an outcome of the Post-Doctoral Fellowship sponsored by the Indian Council of Social Science Research (ICSSR). However, the responsibility for the facts stated, opinions expressed, and the conclusions drawn is entirely of the authors.

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