Emerging Stock Market Integration in the Post Financial Crises Era: An Empirical Analysis of the Short-term and Long-term Linkages

Abstract

In the backdrop of the recent global financial crises in 2008, this article attempts to assess the linkage among Brazil, Russia, India, China and South Korea. For this purpose, we adopted a variety of ways. First, long-run and short-run linkages among emerging market indices were investigated by using Johansen’s co-integration method and Sim’s vector autoregression model. Second, to analyze the issue in detail, we examined the causal relationship and impact of shocks by using Toda and Yamamoto (1995) version of Ganger noncausality test and forecasted error variance decomposition along with the impulse response function. We have investigated short-run causal relationship among the emerging market indices and showed how much of the forecast error variance of NIFTY market returns can be explained by exogenous shocks to the other emerging markets. The results of noncausality test among emerging stock markets indicated that Brazilian market has a unidirectional causality with Indian stock market, and Indian stock market has a unidirectional causality with South Korean market. Finally, the results of variance decomposition and impulse response function suggest that return in Indian stock market (NIFTY) is largely affected by its own shocks, whereas shocks in return of other emerging stock markets do not dominate in case of return in Indian stock market (NIFTY).

Keywords

BRIC-RoK nations stock market integration unit roots test co-integration vector autoregression model variance decomposition impulse response function

Introduction

Financial products can easily be sold and bought in a sound financial market system. Good and strong financial market systems provide shield against any contagion impact of financial crisis. The whole European Union (EU), excluding Russia, is the largest trading partner of Brazil, Russia, India, China (BRIC) and South Korea (Republic of Korea) (BRIC-RoK nations). BRIC-RoK nations are the strategic partner of the EU. After the financial crisis, the EU, by taking motivation from Russia, is now trying to develop deep trading relations with its strategic partners. Now, these emerging market-based economies are lucrative investment destination for the developed countries. The reason behind the foreign direct investment (FDI) flow toward emerging markets from developed capital market was the low cost resources, but now these emerging markets are transforming from cost-effective location for investment to knowledge-based location (UNCTAD, 2006). This is a big reason why the EU is negotiating with its strategic partners to have free trade agreements (FTAs). However, all strategic partners themselves have developed a strategic position in the world economy. Among all strategic partners, India and Brazil are developing economies, and the financial market here is still under the close control of the regulators. Although there is a closed market environment, the corporations, the individuals as well as financial institutions inside and outside the country can buy or sell varied financial products through formal exchange system in these countries. Globalization has exposed the financial markets of these strategic partners to the conditions of the other financial markets, specifically, the stock market. Stock market being the major constituent of the financial market also reacts to global financial economic conditions. How much stock markets of these strategic partners are reactive to each other? This question has attracted the interest of the EU as well as the market players. The wave of the industrialization has increased the volume of the industrial securities market on the stock exchanges of these countries. Contemporary trend in global market has made these strategic partners of EU to form some political and economic agreements in order to facilitate the trade and development of industries among them. China, Russia, and South Korea occupy a big share in the manufacturing sector, and the economies of these countries are well-established industrial economies. Now, the major point of attraction here is to explore the level of the integration among the stock markets of these strategic partners of EU who are newly industrialized countries (India and Brazil) and well-industrialized countries (Russia, China, and South Korea). No doubt the separate coalition among these strategic partner countries of EU has opened up the doors for growth and advancement, but on the other hand, the social, political, and economic conditions of these countries may influence the industry as well as industrial securities market of each other. In context of stock market, it is the prices of the securities that spell the tenor of the stock market. A number of shares of different corporate entities are traded in the stock market at different prices. Hence, it is very difficult to capture the behavior of the stock market just based upon the share prices of a single corporate entity, but the stock market index exhibits the average behavior or the reaction of all securities traded on the exchange. It can be said that the stock market index spells the tenor of the stock market. If we have to explore the impact of the trade coalition among the strategic partners of EU, with respect to stock market, then the stock market index of the group countries should be taken into consideration. No doubt the BRIC-RoK nations are different from each other on economic front but their potential and share in the world market cannot be ignored. The responsiveness of the stock markets of BRIC-RoK nations to each other can easily tell both the short-term and long-term relation among these nations. Indian stock market has already been found integrated with developed American capital market (Bhattacharya & Samantha, 2001) and with the capital market of some south Asian countries (Nath and Verma, 2003; Mukherjee and Mishra, 2005). Due to globalization and openness of the market, now the markets tend to show a lead and lag relationship with each other. In the Indian capital market, the activities of FII (Foreign Institutional Investor) have improved in the last decade and the market has become more responsive. India has a number of trade alliances which has helped India to have an improved and more opened trade with Brazil, Russia, China, and South Korea. However, the quest here lies in examining the responsiveness of the rest of the strategic partner countries of EU to Indian stock market as well as to each other.

EU Strategic Partners (BRIC-RoK) and their Stock Market Index

The strategic partners of EU, the BRIC-RoK nations, are emerging market-based economies. The BRIC countries are making efforts to improve capital market functioning with the member countries. They have created a benchmark equity index derivative. The objective behind this was to make the investors of one member country to bet on the stock market performance of the other member countries. South Korea is a big foreign direct investor in China and now it has established its manufacturing units in India as well. The economic relation of South Korea with India and China has improved, whereas the participation of South Korea in EU has reduced after the debt crisis.

Keeping the same fact in mind, it is logical to make out that the stock market investors of BRIC-RoK nations are now exposed to each other’s stock market conditions due to strong economic linkages. Only the stock market index which can converse about the maximum sectors of the economy or can represent the total corporate sector would be able to explore the thread of integration among the stock markets of BRIC-RoK nations. For the same reason, the following stock market indexes have been considered.

BOVESPA—Brazil

The Brazilian stock exchange is the largest stock exchange in the world in terms of market capitalization. It is a leading stock exchange in Latin American region. On this stock exchange, the market index “IBOVESPA” is the oldest index. The index is a composition of most representative companies in terms of market capitalization and traded volume. The index is representing the market since 1968. The strength of the index is the depiction of most representative companies in the market.

RTS–Russia

The Russian Trading System (RTS) index of Moscow stock exchange is the capitalization weighted composite index. The index is made of 50 most liquid Russian stocks. The index is a free float capitalization weighted index. Stocks in the index are included on the basis of three months rolling review.

KOSPI–South Korea

It is a stock index number of South Korean stock market. It is a composite stock price index of all common stocks, calculated on the basis of market capitalization. The index was broadcasted in 1983 with a base value of 100. Representation of all traded common stock is the strength of this Index.

CNX S&P NIFTY–India

It is the benchmark stock index number of National Stock Exchange (NSE), India. It covers 22 sectors of the economy. It includes 50 most liquid stocks in the composition. It is also free float market capitalization weighted index. Earlier, the index calculation was based on full market capitalization but now it is calculated on the basis of free float methodology. Due to the agreement with the Standard & Poor’s (S&P) financial services, the index is named as CNX S&P NIFTY. Representation of financial services and industrial manufacturing sector with liquid stocks is the strength of the Index.

SSE Composite–China

The index is composed of all stocks (both A and B shares) traded on Shanghai stock exchange. The index is calculated on the basis of Paasche weighted composite price index. The index exists since 1991. The inclusion of all traded stocks in the construction of index makes this index a good representative of the market behavior.

The remaining article is organized as follows: First, we review the related literature. Then, we describe the research gap and then explain the rationale of the study. Next, we outline the major objectives of the study. Then, we present the data source, empirical model, and methodologies. Next, we talk about the estimation results. And finally, we provide the conclusion of the study.

Literature Review

In the past 2–3 decades, the financial markets, particularly the stock market, of those countries which have business and economic association have become more closely interlinked. These markets are converging nowadays irrespective of the market size, financial instruments, financial setup, financial regulations, and so on. It is not only the business and economic association, but also the technological developments in trading systems and communications and the introduction of innovative financial products that is accountable for international stock market linkages and its relation with stock market dynamism.

Earlier studies related to global financial linkages were motivated by the objective of portfolio diversification (Agmon, 1972; Becker, Finnerty, & Gupta, 1990; Grubel, 1968; Hamao, Masulis, & Ng, 1990; Hilliard, 1979). The studies were majorly focused on some developed economies such as USA, UK, Japan, and so on. There are studies on Asian stock market on the same theme. Among Asian countries, India, China, Japan, and South Korea (RoK/Republic of Korea) are the major economies. The stock markets of these countries offer gain on portfolio diversification but for short-term horizon (say weekly and fortnightly) not for long-term horizon (Tiwari, Dar, Bhanja, & Shah, 2013). In order to have gain from portfolio diversification from Asian region, investors should focus on South Korean market because it has a significant impact on all other markets in the region (except China). The portfolio investors suggested to being extra cautious in their investment decisions related to Thailand because it is the most endogenous market in the Asian region, followed by the Indonesia and Malaysia (Raju & Khanapuri, 2009). The stock markets of some advanced and developed countries of EU have also been found highly integrated with the stock markets of developed countries like US and UK (Agmon, 1972; Hilliard, 1979) and offering diversification gain to the investors.

It was not only the portfolio diversification, but also the contagion financial crises of developed countries that made researchers to explore the financial integration. The financial integration among the markets increased after 1987 crash (Arshanapalli, Doukas, & Lang, 1995; Liu, Pan, & Shieh, 1998). The next crisis situation which occurred in 1997 influenced the global integration of stock markets of ASEAN group (Janor, Ali, & Shaharudin, 2007). Among Singapore, Taiwan, India, China, Argentina, Brazil, Malaysia, Hong Kong, and Korea, the level of the long-term association has significantly fallen after the financial crisis of 2008 (Rastogi, 2013).

After liberalization of the financial market in India, the Indian stock market has exhibited a high integration with the stock markets of developed countries (Narayan, Smyth, & Nandha, 2004) like USA, UK, and Japan. Later on, the Indian stock market evidenced, integrated by different studies, with the Asian stock markets such as Indonesia, Malaysia, Philippines, Korea, and Thailand (Mukherjee & Mishra, 2005) and US stock market, but not with Japan, UK, and China (Tripathi & Sethi, 2010). Indian stock market exhibit co-movement with the stock markets of USA, Brazil, Mexico, and China (Joshi, 2011) and despite this, the speed of the adjustment of Indian stock market is higher in comparison to the stock markets of USA, Brazil, Mexico, and China (Joshi, 2011; Verma & Rani, 2015).

Return from Indian stock market lead by the return of major stock index of United States and Japan; and in like manner by the stock market index of other Asian markets, namely, Hong Kong, South Korea, and Singapore (Mukherjee & Bose, 2008). India is an important member of BRIC as well as it has initiated dialogue with South Korea to attract FDI in India.

On the basis of the literature, it is held that the stock market of BRIC nations have some sort of co-movement. South Korea is very close to China and India, and hence, it is assumed that RoK stock market has also some amount of integration with BRIC group. It has been found in recent research that co-movement of the stock market of the BRIC nations with the developed economies (Canada, Russia, and Australia) of their respective region and leading industrialized economies (UK, Germany, and Japan) is not direct. It depends upon the time and is influenced more by the regional aspect (Lehkonen & Heimonen, 2014). The stock markets of BRIC economies are well-integrated with the developed stock markets of USA, UK and Japan (Chittedi, 2010). However, among BRIC countries, in the short run, Indian stock market is dominated by US market, Russian stock market is dominated by Japan market, and rest are dominated by neither (Jeyanthi, 2010).

Correlations and the integration among stock markets is time varying (Longin & Solnik, 1995; Bekaert & Harvey, 1995). It is not only the mere integration, but the degree of stock market integration that is dynamic from one market to another market (Abid, Kaabia, & Guesmi, 2014).

Despite this, the stock markets of emerging market-based economies (BRIC economies) offer higher return than the industrial markets (Buckberg, 1995). The stock markets of China and India are predictable in terms of return and invariable to the unit of measurement, whereas the predictability of stock markets return for Brazil and South Africa depends upon the currency units of measurement. The volatility of return in all the BRIC nations, except Brazil, decays soon (Adua, Alagidedeb, & Karimuc, 2015).

Research Gap

There are good numbers of studies that examine the stock market integration, co-movements, and correlation among BRIC nations, but the integration among BRIC nations and RoK has never been studied. In the same dimension, the impact of the shocks has also never been examined. Therefore, the study is a noble effort to explore the same new dimension.

Rationale of the Study

The debt crisis was contagion. Developed and developing economies both were in problematic state of affairs due to it. EU was the centre of the crisis. The leading Asian economies (China, India, and South Korea) and Brazil are strategic partner of EU. So, the study of integration would be helpful for the policy makers in framing suitable policies for their economies in order to develop safeguard against such contagion financial crisis. The BRIC-RoK is an effective group which can create some policy measures by looking at the level of integration among them in order to cope with any contagion financial crisis. Besides it, the international investors can have gain from portfolio diversification if the level of integration among these promising stock markets would be expressed. Investors can decide their strategies for both long-term and short-term horizon. The stock market integration will help the international investors in unifying these economies and will provide them unrestricted opportunity to participate in the stock market of these countries.

Objectives

The literature review directs us toward the achievement of the following main objectives:

To examine the long-run linkage among emerging stock markets.

To examine the short-run linkage among emerging stock markets.

To ascertain whether there is a causal and effect relationship among the Indian stock market and other emerging nations’ stock markets.

To gauge the effect of exogenous innovations of the emerging stock market variables on the Indian stock market variable.

Data and Empirical Methodology

Description of Sample Price Indices

The sample comprises the daily closing values of the leading stock indices of emerging nations, namely, BOVESPA of Brazil, RTS index of Russia, CNX S&P NIFTY of India, SSE Composite of China, and KOSPI Composite of South Korea from January 1, 2009 to December 31, 2014. The paramount data sources for the study were Bloomberg database and NSE India database (for details, see Table 1).

Table 1.

Data Description

Country	Stock Indices	Abbreviation	Source of Data
India	CNX S&P NIFTY 50	NIFTY	www.nseindia.com
Brazil	IBOVESPA	NIKKEI	www.bloomberg.com
Russia	RTSI	FTSE	www.bloomberg.com
China	SSE Composite	SSE	www.bloomberg.com
South Korea	KOSPI Composite	KOSPI	www.bloomberg.com

Dates from earlier years (i.e., 2009) were not taken into consideration, as the study primarily aims to identify linkages among the emerging stock indices during the post-2008 crises era. Data were collected based on its availability, and all the five indices series were sorted according to the matching trading dates, that is, data were collected on the identical dates across the stock exchanges. The total number of observations is 1,251 in each series.

Empirical Methodology

Variable Transformation and Return Evaluation

All the closing index values were transformed into log form to smoothen out the fluctuations, that is to make the data series linear, and for further analysis purpose. The difference of the closing index values for two consecutive trading days in the natural logarithm form was taken to evaluate the daily returns. It can be depicted as:

R_{t} = log (P_{t} / P_{t - 1}) o r R_{t} = \log (P_{t}) - log (P_{t - 1})

(1)

Here,

R_t = Logarithmic value of the daily return at time t

P_t and P_t–1 = Daily stock index value at two successive days: t and t–1, respectively.

For ascertaining preliminary know-how of behavioral characteristics of the data, summary statistics of all the return indices have been evaluated (see Table 2). At the next phase of preliminary analysis, the Karl Pearson correlation method has been used to identify the degree of association among emerging market return indices variables. As the correlation is not an impeccable measure to determine the association, for the specified purpose, other precise measures have also been used in the study at the later stage.

Table 2.

Descriptive Statistics of Daily Returns for Emerging Markets Indices (2009–14)

	NIFTY	BOVESPA	RTSI	SSE	KOSPI
Mean	0.00078	0.00013	0.00018	0.00039	0.00038
Median	0.00074	0.00002	0.00062	0.00027	0.00062
Maximum	0.16334	0.06513	0.13246	0.05936	0.05739
Minimum	–0.08017	–0.08431	–0.13255	–0.06983	–0.08568
Std. Dev.	0.01424	0.01614	0.02213	0.01451	0.01267
Skewness	1.02290	–0.03410	–0.09444	–0.19084	–0.59335
Kurtosis	18.13527	5.01902	6.91038	5.25170	7.54237
Jarque–Bera	12158.77000	212.72660	798.90640	271.87650	1148.90600
Probability	0.00000	0.00000	0.00000	0.00000	0.00000
Observations	1251	1251	1251	1251	1251

Source: Authors’ own.

Unit Root Test

The meticulous analysis began by providing the univariate properties of the variables of interest by using standard Augmented Dickey–Fuller (ADF) test and Phillip–Perron (PP) test to establish the order of integration of all variables. Three different specifications of ADF tests and PP tests are available. The first excludes both the trend and the intercept term, the second specification includes the intercept term but excludes trend term, and the third specification includes both the trend and the intercept term. Simultaneously, the selection of appropriate lag order is extremely important. A unit root test is a statistical test for the proposition that the autoregressive parameter is one in an autoregressive statistical model of a time series. The pioneering work related to the testing of unit root in time series was done by Dickey and Fuller (1979, 1981). Variable series that contains unit root is considered to be nonstationary. It is considered as stationary time series when mean, variance, and covariance remain unchanged by the time change.

This test is based on the following regressions:

Δ y_{t} = α_{0} + α_{1} t + β y_{t - 1} + \sum_{j = 1}^{k} γ_{j} Δ y_{t - j} + ε_{t}

(2)

Here,

Δ = Difference operator

ε_t = Stationary random error at time t

y_t = Denotes index series at time t

For an index series y_t, the ADF test consists of a regression on the first difference of the series against the series lagged k times. The null hypothesis is that Y_t is nonstationary series, and it is rejected when β is significantly negative. The acceptance of null hypothesis implies nonstationarity.

In case of ADF test, it is assumed that the errors are statistically independent and have a constant variance, while in the PP tests the error disturbances are allowed to have some correlation and heteroskedasticity.

y_{t} = α_{0} + α_{1} y_{t - 1} + a_{2} (t - \frac{T}{2}) + u_{t}

(3)

Here,

y_t = Index series at time t

t = t statistics

T = Sample size

U_t = Random error at time t

Time series data are generated by y_t = y_t–1 + u_t where E(u_t) = 0 for all t.

The constant and the trend terms are retained only if they are significantly different from zero. ADF test establishes optimal number of lags k, by using the Akaike information criterion (AIC), and PP test establishes bandwidth by using Bartlett kernel. It is possible to transform nonstationary to stationary time series either by differencing or de-trending.

Co-integration Test

At the subsequent stage of the study, we have adopted co-integration technique developed by Johansen (1991) to examine the presence of long-run relationship among emerging market’s return indices. This technique is employed to find out the linear combination of integrated variable that is stationary (it is likely that a linear combination of two or more time series can be stationary, despite variables are individually nonstationary). The technique is applied when all the variables are nonstationary at level and integrated of same order. The autoregressive representation for the vector X is shown in the Equation 4.

X_{t} = B_{0} + \sum_{j = 1}^{p} B_{j} X_{t - j} + ε_{t \dots .}

(4)

Here,

X_t = (n×1) column vector of p variables

B = (n×1) vector of constant terms

K = Lag length

B_j = (n×n) matrix of coefficients

ε_t = Disturbance term independently and identically distributed with zero mean and constant variance.

The above vector autoregressive (VAR) process can be re-parameterized and turned into a vector error correction model for using Johansen’s test. It can be represented in the following manner:

Δ X_{t} = B_{0} + \sum_{j = 1}^{p - 1} Γ_{j} Δ X_{t - k} + \prod^{​} X_{t - k} + ε_{t}

(5)

Γ_{j} = \sum_{i = j + 1}^{p} B_{j} and Π = - I + \sum_{i = j + 1}^{p} B_{j}

(6)

Here,

Δ = Difference operator

I = (n × n) identity matrix

Γ and Π = coefficient matrices.

ΔX_t and ΔX_t–j are I(0), and X_t is I(1). I(0) means integrated at level and I(1) means integrated of order one. The Π can be interpreted as coefficient matrix and it is known as the impact matrix. It contains information about the long-run relationships. The determination of the unique co-integrating vectors of X_t in Equation 5 can be done by using estimated equation residuals, that is, two likelihood ratios (LR) test statistics. Johansen’s method to test for the number of characteristic roots has two test statistics for co-integration. The first test, which considers the hypothesis that the rank of Π is less than or equal to r (the number of co-integrating vectors), is based on the trace test statistic (λ_trace) given through

λ_{trace} (r) = - T \sum_{i = r + 1}^{n} l n (1 - λ_{i})

(7)

Here,

λ_i = Estimated values of characteristic roots or the eigenvalues

T = Number of usable observations

N = Number of variables.

The second test is known as the maximal eigenvalue test statistic (λ_max). λ_max test assess the null hypothesis that there are exactly r co-integrating vectors in X_t. It is given by

λ_{max} (r + 1) = - Tln (1 - λ_{r}) .

(8)

The asymptotic critical values for these LR tests are calculated through numerical simulations (see Johansen & Juselius, 1990). If the test statistics is greater than the critical value from Johansen’s table, reject the null hypothesis.

Vector Autoregression (VAR) Test

Seminal work of Sims’s (1980) VAR approach is also adopted in the study to examine short-run linkage among time series variables, and this technique is helpful as it treats all the variables symmetrically. This approach has determined the short-run linkages among emerging market return indices. All the variables are stationary in the model is the elementary assumption of VAR model and it is imperative to identify appropriate lag length. In the two variable conditions, x and y, consider that time path of the y_t be affected by current and past realizations of x_t sequence and time trail of the x_t sequence be affected by y_t sequence (Enders, 2003). It is assumed that both x_t and y_t are stationary. The equations of bivariate system can be symbolized in the following manner:

x_{t} = b_{10} - b_{12} y_{t} + γ_{11} x_{t - 1} + γ_{12} y_{t - 1} + ε_{x t}

(9)

y_{t} = b_{20} - b_{21} x_{t} + γ_{21} x_{t - 1} + γ_{22} y_{t - 1} + ε_{y t}

(10)

Here,

γ₁₁, γ₁₂, γ₂₁, and γ₂₂ = Coefficient of lag variables

b₁₀ and b₂₀ = Coefficients of constants

–b₁₂ and –b₂₁ = Contemporaneous of unit change of y_t on x_t and x_t on y_t respectively

ε_xt and ε_yt = Error term of both equations.

In this theoretical framework, it is supposed that both error terms are white-noise disturbances. This case in point is simple two-variable first-order VAR. In the instance of more number of variables, the number of equations and variables also upsurges. Optimize lag length can be identified through subsequent residual diagnostics.

Toda and Yamamoto Technique of Granger Causality

To ascertain the direction of causal relationship between the variables, we have used Toda and Yamamoto version of Granger Causality, proposed by Toda and Yamamoto (1995). This technique suggested the alternative procedure to test causality, and it has advantage over other causality test. This technique uses a modified Wald (MWALD) test to examine the restriction on the parameters of the VAR (k) model, k being ideal lag length of the VAR model. When a VAR (k + d (max)) is assessed with k degree of freedoms in the bound, it follows asymptotic chi-squared distribution. The highest order of integration for the return series in the system is d(max). This procedure application requires two steps to be followed. The identification of the optimal lag length (k) and the maximum order of integration (d) of the variables in the system is the first step. Different criteria, namely, Schwarz information criterion (SC), AIC, and Hannan–Quinn information criterion (HQ), can be used to ascertain the apt lag structure of the VAR model. After determining the order of integration d(max) and VAR (k), at the following phase, VAR can then be determined with a total of p = (k + d (max)) lags. At the second step, it is required to apply standard Wald tests to the matrix of the first k VAR coefficient. In the subsequent Wald test, the coefficients of the extra lagged terms are not included to demeanor inference on Granger causality. This model tests the null hypothesis that the Ganger noncausality exists between x_i and y_i variable and vice versa.

Impulse Response Function and Variance Decomposition (VD)

To trace out the time path of the various shocks, impulse response function can be useful to determine the relationship among variables after fitting the appropriate VAR system. Equation 11 shows the VAR standard form.

z_{i} = B_{0} + B_{1} z_{t - 1} + e_{t .}

(11)

Here,

z_t = Vector of variable series

B₀ = Vector of “constant coefficients matrix multiplied with inverse coefficients of sequence matrix.”

B₁ = Vector of “matrix of coefficient of lag variables multiplied with inverse coefficients of sequence matrix.”

e_t = Vector of “white noise disturbance matrix multiplied with inverse coefficients of sequence matrix.”

Vector Moving Average (VMA) is represented in Equation 12.

z_{i} = µ + \sum_{i = 0}^{\infty} B_{1}^{i} e_{t - i}

(12)

Here μ = {[\bar{x} \bar{y}]}^{'}

(13)

VMA equation represents x_t and y_t expressed in terms of current and past values of the two types of shocks—e_1t and e_2t. Consider the impulse response function

\begin{array}{c} [\begin{matrix} x \\ y \end{matrix}] = [\begin{matrix} \bar{x} \\ \bar{y} \end{matrix}] + \sum_{i = 0}^{\infty} [\begin{matrix} Φ_{11} (i) & Φ_{12} (i) \\ Φ_{21} (i) & Φ_{22} (i) \end{matrix}] [\begin{matrix} ε_{x t - i} \\ ε_{y t - i} \end{matrix}] \\ z_{i} = μ + \sum_{i = 0}^{\infty} Φ_{i} ε_{t - i} \end{array}

(14)

The coefficients of Φ_i can be used to produce the shocks of ε_xt and ε_yt on the full-time paths of variable sequence, shown in the matrix representation of impulse response. Φ_i in Equation 14 is the impact multiplier matrix (Enders, 2003).

The use of variance decomposition is the other imperative aid in the interpretation of VAR. The proportion of σ_y(n)² due to shocks in the (ε_xt) and (ε_yt) sequence are

\frac{σ_{x}^{2} [Φ_{11} {(0)}^{2} + Φ_{11} {(1)}^{2} + ... + Φ_{11} {(n - 1)}^{2}]}{σ_{y} {(n)}^{2}}

and

\frac{σ_{y}^{2} [Φ_{11} {(0)}^{2} + Φ_{11} {(1)}^{2} + ... + Φ_{11} {(n - 1)}^{2}]}{σ_{y} {(n)}^{2}}

Here,

Σ_x(n)² = n-step-ahead forecast error variance of y_{t + n.}

σ_x² and σy² = Variance of x and y sequence, respectively.

Φ_jk(0) = Impact multipliers for i = 0.

It can be possible to decompose the n-step-ahead forecast error variance into the fragments due to each shock. This method assists in determining the proportion of movement in a sequence due to its own shocks versus shocks to the other variable (Enders, 2003).

Empirical Results and Discussions

The daily stock indices values of Brazil (BOVESPA), Russia (RTS), India (CNX NIFTY), China (SSE Composite), and South Korea (KOSPI Composite) were depicted through graphical representation over the period of the study (see Figure 1). Primary vertical axis displays stock price movement of NIFTY, SSE Composite, RTSI, and KOSPI Composite, and auxiliary secondary vertical axis displays BOVESPA’s stock price movement. Visually, it can be interpreted from the graph that all these indices were recovering after post-2008 global financial crises era. Emerging market indices were moving in tandem in a long run, majorly from 2009 to 2013, but subsequently most of these indices have shown swift positive and negative trend movement.

Figure 1.

Source: Authors’ own.

The detailed descriptive statistics of all emerging market return indices are reported (see Table 2), and it has been observed that all these indices have produced a positive average daily return for the duration of the study period. NIFTY has provided highest positive average daily return among these emerging nations from 2009–14. Standard deviation (SD) of indices returns shows that KOSPI has the smallest variability, followed by NIFTY, and RTSI has highest variability among the emerging nations. NIFTY return was positively skewed over the time period of the study, while returns of other emerging markets were negatively skewed. Jarque–Bera Test statistics for all emerging markets indicates that the distribution of all these return series is nonnormal.

Correlation Analysis Results

Pearson correlation analysis is used in the study (see Table 3) to identify the degree of association between emerging market returns indices. Correlation of NIFTY returns is found highest with RTSI returns (r = 0.4250) and showed similar kind of association with KOSPI returns (r = 0.4170). NIFTY returns correlation coefficient with BOVESPA returns is 0.3110, while its least correlation is found with SSE Composite returns (r = 0.2542). It can also be inferred from correlation matrix that among all indices, RTSI and BOVESPA returns has highest correlation coefficient (r = 0.4407), and BOVESPA and SSE Composite returns have lowest correlation coefficient (r = 0.2007). All correlation coefficient values are significant at 1 percent level.

Table 3.

Pearson Correlation Analysis of Daily Returns (2009–14)

	NIFTY Return	BOVESPA Return	RTSI Return	SSE Return	KOSPI Return
NIFTY Return	1.0000
BOVESPA Return	0.3110(0.0000)*	1.0000
RTSI Return	0.4250(0.0000)*	0.4407(0.0000)*	1.0000
SSE Return	0.2542(0.0000)*	0.2007(0.0000)*	0.2421(0.0000)*	1.0000
KOSPI Return	0.4170(0.0000)*	0.2898(0.0000)*	0.4123(0.0000)*	0.3645(0.0000)*	1.0000

Source: Authors’ own.

Notes: 1. Figures in square brackets are probability values (p-values) and all p-values are two-tailed.

2. Asterisks (*) denotes rejection of the null hypotheses at 1 percent significance level.

3. For the Pearson Correlation, the null hypotheses are “the correlation coefficient is equal to zero” (i.e., ρ = 0).

Table 4.

Unit Root Tests

Variables	ADF Statistics	ADF Statistics	PP Statistics	PP Statistics
Variables	at Level	at First Difference	at Level	at First Difference
LNSE	–2.8132	–10.8428	–1.8411	–34.4521
LNSE	(0.0567)	(0.0000)*	(0.3607)	(0.0000)*
LBOVESPA	–2.5377	–36.2159	–2.4895	–36.2644
LBOVESPA	(0.1068)	(0.0000)*	(0.1182)	(0.0000)*
LRTS	–2.3723	–32.0346	–2.3265	–32.0556
LRTS	(0.1499)	(0.0000)*	(0.1637)	(0.0000)*
LSSE	–1.7003	–34.9615	–1.7686	–34.9738
LSSE	(0.4309)	(0.0000)*	(0.3964)	(0.0000)*
LKOSPI	–2.9504	–9.9843	–2.6734	–36.8168
LKOSPI	(0.1470)	(0.0000)*	(0.2480)	(0.0000)*

Source: Authors’ own.

Notes: 1. Asterisks (*) denote rejection of the null hypothesis at 1percent significance level.

2. The null hypotheses are series contain unit root.

3. Figures in square brackets are probability values.

4. ADF is the Augmented Dickey–Fuller test and PP is the Phillips–Perron test.

Unit Root Test Results

For analyzing the existence of long-run linkages among emerging stock market indices, it is desirable to perform Johansen co-integration method. But before that, it is essential to determine the order of integration of all variables. The log form of the indices series is denoted as LBOVESPA, LRTS, LNSE, LSSE and LKOSPI. The two unit root test, ADF test, and PP test are used to examine the stock indices’ nonstationarity. These tests are applied after determining the appropriate lag structure and bandwidth, as indicated by AIC for ADF test and Bartlett kernel for PP test, respectively. The results of the ADF test and PP test for unit root test (see Table 4) show that all the variable series are nonstationary at level. However, the series are stationary at their first difference, that is, all the series are integrated of Order one I(1).

Indispensable subsequent phase, before moving to co-integration approach, is the identification of optimal lag length. We employed three different criteria, namely AIC, SC, and HQ, and the results of length selection criteria indicate two lags as optimal lag length value (see Table 5).

Table 5.

Lag Length Selection Criteria

Lag	AIC	SC	HQ
0	–7.7050	–7.6854	–7.6982
1	–28.4174	–28.2937	–28.3709
2	–28.6071*	–28.3804*	–28.5218*
3	–28.6034	–28.2738	–28.4795
4	–28.5814	–28.1488	–28.4187
5	–28.5640	–28.0283	–28.3626
6	–28.5655	–27.9268	–28.3254
7	–28.5615	–27.8197	–28.2826
8	–28.5491	–27.7044	–28.2315

Source: Authors’ own.

Notes: 1. Asterisks (*) indicates lag order selection by the criterion.

2. AIC is the Akaike information criterion, SC is the Schwarz information criterion and HQ is the Hannan-Quinn information criterion.

Co-integration Analysis Results

Co-integration analysis is used to determine whether the five emerging market nonstationary price indices share a common stochastic trend in the long run or not, that is long-run relationship among the variables series is investigated by assessing the five emerging market series for co-integration. The order of the stationary I(1) is the same for all five variables, and we used Johansen multivariate co-integration test to identify the order of co-integration d (max). The null hypothesis is tested by using the Trace test as well as Maximum Eigenvalue test.

The hypothesis which posits that there is co-integration relationship among BOVESPA, RTSI, NIFTY, SSE, and KOSPI is not accepted at 5 percent level of significance (see Table 6). There is no significant co-integrating rank among emerging market indices, and it has been confirmed by both Trace statistic and maximum Eigenvalue statistics. This indicates the nonexistence of the long-run equilibrium relationship among the BRIC and South Korean markets.

Table 6.

Johansen Co-integration Test among Emerging Market Indices

Null Hypothesis	Trace Statistic	Max-Eigen Statistic
H0: r = 0	69.3498 (0.1654)	28.7133(0.2227)
H0: r ≤ 1	40.6365(0.4388)	20.5662(0.3701)
H0: r ≤ 2	20.0703(0.7223)	9.0593(0.9004)
H0: r ≤ 3	11.0111(0.5410)	7.4099(0.6193)
H0: r ≤ 4	3.6012(0.4747)	3.6012(0.4747)

Source: Authors’ own.

Notes: 1. r denotes the number of co-integrating vectors. Critical values of the test statistic are represented by numbers in parentheses next to r = 0 until r ≤ 5 at 5 percent significance level.

2. Figures in square brackets are probability values (p-values).

3. The null hypothesis is that there is no co-integration at 5 percent significance level.

Vector Autoregression (VAR) Results

In this section, we tried to explore whether the five price return indices share a common stochastic trend in the short run or not with the help of VAR model of the daily indices returns with 2 selected as optimum lag length for the model, (see Appendix for VAR Residual Diagnostic results). The estimation of emerging markets short-run linkage in the study is obtained by the following VAR model:

N I F T Y_{t} = β_{0} + \sum_{j = 1}^{2} β_{1 j} N I F T Y_{t - j} + \sum_{j = 1}^{2} β_{2 j} B O V E S P A_{t - j} + \sum_{j = 1}^{2} β_{3 j} R T S I_{t - j} + \sum_{j = 1}^{2} β_{4 j} S S E_{t - j} + \sum_{j = 1}^{2} β_{5 j} K O S P I_{t - j} + u_{i t}

Here, NIFTY_t is a return index at time t value, β₀ represents constant in the model, β_1j, β_2j, β_3j, β_4j, and β_5j are the coefficients of the model, NIFTY_t–j, BOVESPA_t–j, RTSI_t–j, SSE_t–j, and KOSPI_t–j represents coefficients of return lag variables, and u_ij is the residual series of the whole VAR model. VAR model specification of emerging market indices return indicated that second lagged value of NIFTY has impacted NIFTY returns in the short run at 5 percent level of significance. Both, first and second, lagged values of BOVESPA have impacted NIFTY returns in the short run at 1 percent level of significance (see Table 7). Coefficient of the VAR model is significant at 5 percent level. Adjusted R² value of VAR model is 5.612 percent or 0.5612, and its F-statistic value is also significant at 1 percent level.

Toda and Yamamoto Procedure of Granger Causality Results

After inspecting the long-run and short-run linkages, we further study causality among emerging markets by using alternative approach, i.e., estimating Granger causality test by using the Toda–Yamamoto (1995) procedure. The Toda and Yamamoto (1995) augmented the Granger causality test and it has been obtained in the present study by estimating the VAR model. The optimal lag length was 2 for VAR model in the study and then, we estimated a system of VAR at levels, using total lag length 3 (dmax (1) + k (2)).

The analysis concentrated on finding the unidirectional and bidirectional causal relationship between India’s stock market and other emerging stock markets. The results concluded that there is unidirectional causality run from Brazilian stock market, but not from the Russian, Chinese, and South Korean stock markets, to the Indian stock market at 1 percent significance level. The results also found unidirectional causality run from Indian stock market to South Korean stock market at 5 percent significance level, but there was no causality run from the Indian stock market to any of the other emerging stock markets, namely Brazilian, Chinese, and Russian markets (see Table 8).

Table 7.

Vector Autoregression (VAR) Model of Emerging Market Indices Return

Coefficient	β11	β12	β21	β22	β31	β32	β41	β42	β51	β52	β0
Coefficient Values	–0.0388	–0.0706	0.2337	0.0832	–0.0050	0.0189	–0.0413	0.0024	–0.0622	–0.0246	0.0010
t-Statistic	–1.2005	–2.2137*	8.3846**	2.8526**	–0.2346	0.8723	–1.4260	0.0813	–1.6133	–0.6653	2.4763*
Adjusted r-squared = 0.05612
F-statistic = 8.41967**
Prob (F-statistic) = 0.00000

Source: Authors’ own.

Notes: 1. Subsequent asterisks (**) and (*) denotes rejection of the null hypotheses at 1 percent and 5 percent significance level, respectively.

2. For βij, the null hypotheses are “the correlation coefficient is equal to zero” (i.e., ρ = 0) and for F-statistic, the null hypotheses is “the r-square value is not significant (i.e., r-square is equal to zero).”

Table 8.

Test for Granger Causality Applying the Toda–Yamamoto MWALD Test

Variable	Causality	Chi-square Value (χ²)	Prob. Value
BOVESPA	BOVESPA→NIFTY	70.6442**	0.0000
BOVESPA	NIFTY→BOVESPA	4.5415	0.1032
RTS	RTS→NIFTY	0.6036	0.7395
RTS	NIFTY→RTS	2.6167	0.2703
SSE Composite	SSE Composite →NIFTY	2.8464	0.2409
SSE Composite	NIFTY→SSE Composite	1.3157	0.5180
KOSPI	KOSPI→NIFTY	2.3518	0.3085
KOSPI	NIFTY→KOSPI	8.1752*	0.0168

Source: Authors’ own.

Notes: 1. → denotes the direction of the Granger causality.

2. Subsequent asterisks (**) and (*) denotes rejection of the null hypotheses at 1 percent and 5 percent significance level, respectively.

3. The null hypothesis is that x does not cause y.

Impulse Response Function and Variance Decomposition Results

In the VAR model, impulse response helps to identify the sensitivity of the dependent variables when a shock is put to the error term. The response of NIFTY returns over 10 periods to shocks in other emerging markets return indices is depicted in Figure 2). Specifically, we are interested to find out the impact of one SD shock to the innovations in current and future values of endogenous variables, that is, to trace out the time path of various shocks on the variables contained in the VAR model of the study. The results of the impulse response function demonstrate that BOVESPA return shows some significant response for shorter period (i.e., 2 days), the response contracts on the third day, and finally, it becomes insignificant in longer period.

Figure 2.

Source: Authors’ own.

The response of RTSI return, SSE return, and KOSPI return to NIFTY return remained insignificant for both shorter period (i.e., 2–3 days) as well as in the longer period (i.e., 10 days).

After examining impulse response results, we lastly confer the results of forecast error variance decomposition, and it is based on Cholesky factorization. In the shorter duration, that is 3 days, impulse to NIFTY index returns account for 93.8044 percent variation of the fluctuation in NIFTY index return (own shock), innovation to BOVESPA index return can cause 5.6417 percent fluctuation in NIFTY index return, innovation to RTSI index return can cause 0.0689 percent fluctuation in NIFTY index return, innovation to SSE index return can cause 0.2838 percent fluctuation in NIFTY index return, and innovation to KOSPI index return can cause 0.2011 percent fluctuation in NIFTY index return (see Table 9). In the longer duration, that is more than a week’s duration, impact of all these shocks remains almost immobile. So, it can also be concluded that NIFTY index return, BOVESPA index return, RTSI index return, SSE index return, and KOSPI index return innovations have almost analogous impact in both short run and long run in NIFTY index return, and NIFTY index return is majorly affected by its own innovation, that is 93.7655 percent (see Table 9).

Table 9.

Variance Decomposition of NIFTY Return

Period	NIFTY Return	BOVESPA Return	RTSI Return	SSE Return	KOSPI Return
1	100.0000	0.0000	0.0000	0.0000	0.0000
2	94.0913	5.4206	0.0347	0.2566	0.1967
3	93.8044	5.6417	0.0689	0.2838	0.2011
4	93.7680	5.6727	0.0707	0.2838	0.2047
5	93.7657	5.6739	0.0719	0.2838	0.2047
6	93.7655	5.6739	0.0719	0.2838	0.2048
7	93.7655	5.6739	0.0719	0.2838	0.2048
8	93.7655	5.6739	0.0719	0.2838	0.2048
9	93.7655	5.6739	0.0719	0.2838	0.2048
10	93.7655	5.6739	0.0719	0.2838	0.2048

Source: Authors’ own.

Conclusion

The present research work is an empirical assessment of the stock market integration for short-term and long-term horizon among the indices of emerging market-based economies that are the strategic partner of the EU. Johansen’s test was applied on the time series data (January, 2009 to December, 2014) to determine the co-integrating relationship among the stock markets of Brazil, Russia, China, India, and South Korea (BRIC-RoK nations). The results of the test (see Table 6) clearly depicted the absence of co-integrating relationship among the stock markets of these countries. In the long run, the diversification of the portfolio will be beneficial for international investors. It is held on the basis of the same results that after the crisis of 2008, the long-term relationship among the BRIC-RoK stock markets has totally evaporated, the findings well support the findings of Chittedi (2009). After it, causality among these stock markets must not be there as per the Engle Granger test of causality, but we used Toda–Yamamoto version of Granger causality. This version of the causality provides freedom to assess the causal relation irrespective level of integration and excluding the co-integration. The results of the test (see Table 8) clearly indicated one-dimensional causality from Brazilian stock market to Indian stock market and from Indian stock market to South Korean stock market. Here, the findings of the study support the findings of Mukherjee and Mishra (2005). From the results, it is derived that Indian stock market bears the impression of Brazilian stock market, but do influence the stock market of Korea. Russia and China do not have co-integration or the causality toward Indian, Brazilian, and South Korean stock market and vice versa. Besides this, the short-run dynamics among these emerging market-based economies analyzed with the help of VAR model. The VAR (see Table 7) model suggest the return of Indian stock market influenced by its own return of the previous day and by the returns of last two consecutive days offered by the Brazilian stock market at 1 percent level of significance. Form variance decomposition, it is revealed that the return in Indian stock market is highly affected (93.8 percent, see Table 9) by its own innovation.

It is concluded that the unidirectional linkage from Brazilian stock market side to Indian stock market is consistent in the short run but not in the long run. In the long run, the linkage among the stock markets of EU’s strategic partners is insignificant. So, the investors of EU as well as rest of the world cannot unify these emerging market-based economies. It is only the diversification strategies which would be helpful for them in order to generate returns from the portfolio that contains investment in the stock markets of BRIC-RoK nations.

Appendix : VAR Specifications

Residual Serial Correlation Test

We have applied residuals diagnostic test to ascertain whether the VAR model is correctly specified or not. Breusch–Godfrey Serial Correlation LM (Lagrange Multiplier) Test with two lags was used to determine the serial correlation issue in the residual series. Probable chi-square value is 0.1822 or 18.22 percent, which is greater than 0.05 or 5 percent level of significance (see Table A.1). Therefore, it can be concluded that there is no significant serial correlation in the residual series of VAR model.

Table A.1.

Breusch–Godfrey Serial Correlation LM Test Results

Obs*R-squared

3.4051

Prob. Chi-Square

0.1822

Source: Authors’ own.

Note: The null hypothesis is that “there is no serial correlation in the residual of this model.”

Residual Heteroskedasticity Test

Four different residual heteroskedasticity tests were applied to identify heteroskedasticity issue in the residual series, namely Breush–Pagan–Godfrey test, ARCH test, White test (without including white cross reference terms) and White test (including white cross reference terms).

Probability value of Breush–Pagan–Godfrey test is 0.6356 or 63.56 percent, ARCH test is 0.7542 or 75.42 percent, White test (without including white cross reference terms) is 0.9428 or 94.28 percent, and White test (including white cross reference terms) is 0.9573 or 95.73 percent. Probability values of all these tests are greater than 0.05 or 5 percent (see Table A.2). Therefore, it can be concluded that there is no significant heteroskedasticity in the residual series of VAR model.

Table A.2.

Heteroskedasticity Test Results

	Breusch–Pagan–Godfrey Test	ARCH Test	White Test	White Test(Including White Cross Terms)
Observed R²	7.931067	0.098016	4.099045	46.75748
Probability Chi-Square	0.6356	0.7542	0.9428	0.9573

Source: Authors’ own.

Note: The null hypothesis for all tests is that “there is no heteroskedasticity in the residual series.”

Footnotes

Authors’ Biography

Rajneesh Prakash Verma, is M.B.A.; P.G. Diploma in Computer Applications and currently pursuing Fellow Programme in Management (F.P.M.) in finance from National Institute of Financial Management. He is presently working as Lecturer at Department of Management Studies, NIT-Hamirpur (Himachal Pradesh). He has presented papers in National conference and also has published research paper in peer reviewed journal. His area of research are: Corporate Finance, Financial Markets and International Finance.

Poonam Rani, is M.Com; M.Phil; M.B.A and F.P.M. She has done her F.P.M from National Institute of Financial Management. Poonam Rani is presently working as Assistant Professor at Akal University, Bathinda (Punjab), India. She is Highly Commended Paper Award Winner at University of Mumbai, ADMIFMS IMRC2013-14. She has participated in number of conferences and seminars at national and international level. Her areas of research are: Corporate Finance & Financial Markets.

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