Modelling evolving long-run relationships: The linkages between stock markets in Asia* by José L. Fernández-Serrano** Simón Sosvilla-Rivero*** DOCUMENTO DE TRABAJO 2000-11

March 2000

* The authors wish to thank BBVA for providing the data set. Simón Sosvilla-Rivero gratefully acknowledges financial support by the Spanish Ministry of Education, through DGICYT Project PB98-0546-C02-01.

** Universidad Europea de Madrid.

*** FEDEA and Universidad Complutense de Madrid.

Los Documentos de trabajo se distribuyen gratuitamente a las Universidades e Instituciones de Investigación que lo solicitan. No obstante están disponibles en texto completo a través de Internet: http://www.fedea.es/hojas/publicaciones.html#Documentos de Trabajo

These Working Documents are distributed free of charge to University Department and other Research Centres. They are also available through Internet: http://www.fedea.es/hojas/publicaciones.html#Documentos de Trabajo

ABSTRACT

This paper examines the linkages between the stock markets in Asia during the 1977-1999 period using recently-developed cointegration techniques that allow for structural shifts in the long-run relationship. Our results suggest that, if we apply conventional cointegration tests, we do not find evidence of a long run relationship between the Asian stock markets. In contrast, if we introduce the possibility of structural breaks, we find strong evidence in favour of such relationship between the Taiwanese and Japanese indices from October 1987, while some marginal cointegration is detected between Singapore and Japan until February of 1992 and between Korea and Japan from April 1987.

JEL classification numbers: C22, F36, G15

KEY WORDS: Stock market, Cointegration, Structural change

1. Introduction

After the stock market crash in October 1987, there was a considerable interest in empirical and theoretical investigations of the linkages between asset markets. A decade later, the financial crisis in Asian markets has renewed this interest. This issue is an important concern for investors since greater integration among world markets implies stronger comovements between markets, therefore reducing the opportunities for international diversification. Furthermore, market comovements can also lead to market contagion as investors incorporate into their trading decisions information about price changes in other markets in an attempt to form a complete information set, carrying the risk that errors in one market may be transmitted elsewhere (see, e. g., King and Wadhwani, 1990).

Studies testing for possible international stock market linkages have found conflicting evidence . This can be attributable to the wide range sample periods and sampling frequencies examined, as well as different methodologies employed. Interestingly, most recent studies tend to find greater instability, suggesting that the interrelationships among national stock markets may have undergone a substantial change during the 1980s.

The aim of this paper is to contribute to this growing literature by offering further evidence on long-run relationships between stock markets between Asian countries during the 1977-1999 period. Our study differs from the previously published papers in several ways. First, while most of the studies examine mainly short-run market relationships, we concentrate our attention on long-run relationship among national stock markets. The presence of such long-run relationship means that the diversification would not be effective. Second, we make use of recently-developed cointegration techniques that allow for structural shifts in the long-run relationship. These shifts could be due to changes experienced in those countries during the sample period, such as the movement from being relatively isolated from outside influences to their stock markets being opened up and exchange rates floated, or the recent turmoil in the equity and foreign exchange markets of this region. Third, we focus on geographic integration, examining long-run linkages among Asian stock markets, in contrast with those papers that analyse the linkages between developed and Asian markets. Finally, value-weighted indices from the major stock exchanges are employed (as opposed to price weighted or other indices) as well as the use of daily data.

The paper is organised as follows. The econometric methodology is presented in Section 2, while Section 3 describes the data set and offers the empirical results. Finally, some concluding remarks are provided in Section 4.

Examples of recent empirical studies include the works of Arshanapalli and Doukas (1993), Koch and Koch (1991), Ammer and Mei (1996), Karolyi and Stulz (1996), Lin et al. (1996) and Janakiramanan and Lamba (1998).

2. Econometric methodology

The econometric methodology used in this paper has the following main objectives: (i) to analyse the order of integration of the variables and the stability of the stochastic trend, (ii) to examine the long run relationship between the variables using cointegration techniques, and (iii) to test for parametric instability in the estimated cointegration relations.

To test for unit roots, in addition to the traditional augmented Dickey-Fuller (ADF) test, we use sequential ADF tests in order to detect structural changes in the stochastic trend as well as changes in the degree of integration [Fernández-Serrano and Peruga (1999a y 1999b)]. As it is well known, to test the null hypothesis of a unit root in a time series , the standard ADF test computes the pseudo t-ratio in the following regression:

\[\Delta \mathrm{Y} _ {\mathrm{t}} = \mu + \beta t + \delta \mathrm{Y} _ {\mathrm{t-1}} + \sum_ {\mathrm{i} - 1} ^ {\mathrm{q}} \gamma_ {\mathrm{i}} \Delta \mathrm{Y} _ {\mathrm{t-i}} + \epsilon_ {\mathrm{t}}\tag{1}\]

assuming that there is not any structural change in the parameters and .

The sequential ADF test usually employed in the literature [Banerjee, Lumsdaine and Stock (1992), Zivot and Andrews (1992), Perron and Vogelsang (1992) and Montañés (1996)] involves estimating the following regressions:

\[\Delta \mathrm{Y} _ {\mathrm{t}} = \mu + \mu^ {\prime} \mathrm{D} _ {\mathrm{rt}} + \delta \mathrm{Y} _ {\mathrm{t-1}} + \sum_ {\mathrm{i} = 1} ^ {\mathrm{q}} \gamma_ {\mathrm{i}} \Delta \mathrm{Y} _ {\mathrm{t-i}} + \epsilon_ {\mathrm{t}}\tag{2}\]

where

\[D _ {\tau t} = \left\{ \begin{array}{l l} 0 & t < [ \tau T ] \\ 1 & t \geq [ \tau T ], \end{array} \right. \quad \tau \in (0, 1)\]

is a dummy variable allowing us to locate the break date in each one of the observations in the closed subset of (0,1). For each possible break date in the sample, , two statistics are computed from regression (2): and . is the standard pseudo t-ratio for testing the null hypothesis of a unit root , while is the absolute value of the t statistic for testing the null hypothesis (i.e., it is a test of stability in the stochastic trend). If we impose the existence of a unit root in (2), we have the following restricted regression:

\[\Delta Y _ {t} = \mu + \mu^ {\prime} D _ {c t} + \sum_ {i - 1} ^ {q} \gamma_ {i} \Delta Y _ {t - i} + \epsilon_ {t}\tag{3}\]

and, based on it we can compute .

From regressions (2) and (3), we obtain a sequence of estimated values for each statistic. From this sequence, we take two summary values: the supreme and the man. therefore we compute the following six statistics: , , , , and .

Following Zivot and Andrews (1992), we consider as a breakpoint the observation associated with the corresponding supreme: , and .

Until now, we have assumed that the time series follows a stochastic process that has always the same degree of integration [i. e., changes in the parameter in regression (1) are not allowed]. To consider the possibility that such parameter may not be constant in all the sample (and, therefore, the order of integration of the stochastic process could change depending on the subsample examined), we can study the following set of regressions:

\[\Delta Y _ {t} = \mu + \gamma_ {1} D _ {t r} Y _ {t - 1} + \gamma_ {2} [ 1 - D _ {t r} ] Y _ {t - 1} + \sum_ {i = 1} ^ {k} \delta_ {i} \Delta Y _ {t - i} + u _ {t}\tag{4}\]

\[\Delta Y _ {t} = \mu + \alpha_ {1} [ 1 - D _ {t \tau} ] Y _ {t - 1} + \sum_ {i = 1} ^ {k} \delta_ {i} \Delta Y _ {t - i} + u _ {t}\tag{5}\]

\[\Delta \mathrm{Y} _ {\mathrm{t}} = \mu + \alpha_ {2} D _ {\mathrm{tr}} \mathrm{Y} _ {\mathrm{t-1}} + \sum_ {\mathrm{i} = 1} ^ {\mathrm{k}} \delta_ {\mathrm{i}} \Delta \mathrm{Y} _ {\mathrm{t-i}} + u _ {\mathrm{t}}\tag{6}\]

Regression (4) simultaneously considers both subsamples resulting from the division of the sample using a dummy variable. Since none restriction is imposed in any of the subsamples, this regression tries to test simultaneously the null hypothesis of a unit root against the alternative hypothesis of stationarity in both subsamples. In this way, for example, the time series could be integrated of order one in one subsample and integrated of order zero in the other. In the other two regressions, the existence of a unit root is imposed in one subsample [in the first subsample in regression (5) and in the second subsample in regression (6)], allowing the possibility of the variable being stationarity in the not restricted subsample.

For each possible break point in the sample, the statistics , , , and are then computed. The first two statistics ( and ) test for a unit root in the first or second subsamples, respectively. The statistic tests separately for a unit root in the first subsample, while the statistic does the same in the second subsample. As in the previous case, after finishing this testing procedure, we will have four sequences of estimated statistics and from these sequences we compute the summary statistics: , , , , , , and . In this case, the estimators of the break points are , , and , respectively.

In order to estimate the cointegrating vector and analyse its stability, we have made use of Gregory and Hansen (1996)'s generalization of the usual residual based cointegration tests, that allows for a broader view of cointegration by considering an alternative hypothesis in which the cointegration vector suffers shift at an unknown time. Therefore, we test for a unit root in the residuals of the following cointegrating regression:

\[Y _ {t} = \mu_ {1} + \mu_ {2} D _ {\tau t} + \alpha_ {1} X _ {t} + \alpha_ {2} X _ {t} D _ {\tau t} + \epsilon_ {t}, \quad t = 1,.., T,\tag{7}\]

where is a vector of I(1) regressors and is I(0). Once we have estimated (1) by OLS, we apply the ADF test to the cointegrating residual . For each possible break point we compute the ADF(t) test.

As before, we will have a sequence of estimated statistics and from this sequence we compute the summary statistics: InfADF and MeanADF, being NinfADF the estimator of the break point.

3. Empirical results

In this paper we have used daily closing prices of the five largest Asian stock markets: Hong Kong, Japan, Singapore, South Korea and Taiwan. Specifically, the indices under study are the Hang Seng (HK), the Nikkei 225 Stock Average (J), the Singapore SE Composite (S), the Korea SE Composite (K) and the Taiwan SE Weighted (T), all expressed in terms of local currencies. The data are obtained from BBVA and cover the period 1 January 1977 through 16 November 1999 (5447 observations), except for Singapore where the data spans from 1 February 1986 to 16 November 1999 (3619 observations). It should be notice that all the markets examined trade simultaneously during the day, and therefore the market linkages can be analysed in a more appropriate setting.

Given the importance of the Japanese stock market in the Asian region, we take it as the reference in order to study the linkages between it and the other stock markets. In Figure 1 we present the graphs of the levels of the HK, S, K and T indices together with the Japanese index, while Figure 2 shows the difference of those indexes with the Japanese index.

Table 1 provides summary statistics of the price levels and returns series, while Table 2 gives the correlation coefficients between the stock indices. As can be seen in Table 1, the price level series are positively skewed and strongly serially correlated. The Jarque-Bera (1980) test for joint normal kurtosis and skewness rejects the normality hypothesis. As Table 2 shows, the correlation among various stock markets returns are positively and generally significantly different from zero.

Panel A of Table 3 reports the results for stability in the stochastic trend, while Panel B presents the results for the degree of partial integration. The results are shown for the first different and the levels of the variables. As can be seen, for the level variables the ADF test cannot reject the null hypothesis of a unit root in any stock market at the 5% significance level. On the other hand, for the first differences the ADF test always rejects the null hypothesis of a unit root. These results are corroborated by the sequential statistics Inf tδ and Mean tδ, more robust then the ADF test, except for the Taiwanese index. Furthermore, the restricted statistic of change in the stochastic trend —Sup — suggests certain instability around observation 2869 (28 December 1989) for the Japanese index, while the un restricted statistic Sup detects instability for Taiwanese and Korean indices in observations 2080 (19 December 1986) and 1844 (23 January 1986), respectively. It is interesting to observe that although for the T and K indices the restricted statistics do not suggest instability, the associated estimator for the break point indicates observations 2899 (8 February 1990) and 2675 (31 March 1989), respectively. These observations are consistent with the information obtained from a visual inspection of the graphs for those indices, as shown in Figure 1.

Regarding the results in Panel B of Table 3, for the first differences there is not any sign of change in the order of integration. However, for the level variables, as in the previous case, for the indices of Japan, Korea and Taiwan, we do detect a change in the order of integration. The results from the Supt , Meant , Supt and Meant statistics suggest the Japanese index presents a stationary behaviour from observation 3014 (19 July 1990). For the K and T indices, the Supt and Supt tests (with higher power than those based in the means) detect a change in the order of integration in the second part of the sample, although in the Korean cases the statistic Supt only indicates such a change marginally. For both indices, the break point is situated around the same observation suggested by the tests for stability in the stochastic trend.

In Table 4 we report the results for the difference between each index and the Japanese index. In doing so, we are imposing a cointegrating relation for all sample size. As can be seen in Panel A of Table 4, the traditional ADF test cannot reject the null hypothesis of a unit root in all cases. These results are corroborated by the sequential tests, except for the Taiwanese case, where the Inf statistic shows a contradictory result. Nevertheless, since the null hypothesis of stability in the stochastic trend is rejected by the Sup test, in this case we cannot reject the hypothesis of a unit root either. In Panel B of Table 4 we examine if the imposed cointegrating relations do characterize any subsample. As can be seen, for none of the differentials we can accept that there is a subsample with an order of integration different from that for the whole sample. Only for the difference between the Taiwanese and Japanese indices the statistics Supt and Supt present relatively high values. However, the change in the order of integration cannot be accepted at the usual significance levels from July 1987 (when the statistics Nsupt and Nsupt locate the break point).

Given the results of Table 4, we proceed to analyse if there is cointegration (without imposing it a priori) and if such cointegrating relation is stable. To that end, we make use of the test for cointegration proposed by Engle and Granger (1987) and the stability test in cointegrating relations suggested by Gregory and Hansen (1996). Panel A of Table 5 reports the results of these test for the whole sample. As can be seen, the results of the ADF tests suggest that we cannot reject the null hypothesis of no-cointegration ADF test in any case. On the other hand, the stability tests InfADF and MeanADF only detect evidence of instability for the cointegrating regression between the Japanese and the Taiwanese indices. We also show the break points suggested by the NinfADF statistics. Such break points are used to define two subsamples. It should be noticed that, even though the statistics InfADF and MeanADF are not significant in the cointegrating regressions involving the HK, the S and the K indices, the estimated values (specially the InfADF statistic) could indicate some instability around the observation detected by the NinfADFstatistic.

Panel B of Table 5 reports the results of the cointegration tests for the different subsamples. For the case of Taiwan, there is a full agreement in all the statistics ADF, InfADF and MeanADF regarding the existence of a cointegrating relationship with the Japanese index from October 1987. For the other cases, there is some discrepancy in the cointegration tests. In the cointegrating regression between the indices of Hong Kong and Japan, there is not evidence of a long run relationship in any of the subsamples. Regarding Singapore, all three statistics indicate a marginal cointegration until February of 1992 (significance at the 80% level). Finally, for Korea the ADF statistic suggests a cointegrating relationship with the Japanese index from April 1987 at the 5% significance level.

4. Concluding remarks

In this paper we have provided some new evidence on the relationship between the major Asian stock markets, using daily data covering the 1977-1999 period. We depart from previously published papers by making use of recently-developed cointegration techniques that allow for structural shifts in the cointegration vector.

Our results suggest that, if we apply cointegration tests without structural breaks, we do not find evidence of a long run relationship between the Asian stock markets indices under study and the Japanese index. In contrast, if we introduce the possibility of structural breaks, we find strong evidence in favour of such relationship between the Taiwanese and Japanese indices from October 1987, while some marginal cointegration is detected between Singapore and Japan until February of 1992 and between Korea and Japan from April 1987.

Therefore, the analysis carried out in this paper has provided some evidence in favour of modelling the long-run relationship between Asian stock markets using an evolving formulation that formally considers eventual structural breaks rather than the conventional specification.

The evidence of cointegration between the Asian stock markets provided in this paper would imply that, although it is still possible in this region to derive portfolio diversification in the short run, it is not possible in the long run. As a result, the gains from international diversification for investors with long holding periods may be limited.

On the other hand, as pointed by Caporale and Pittis (1998), cointegration that links different stock markets should be interpreted as evidence of predictability, without referring to the question of market efficiency. Indeed, Dwyer and Wallace (1992) show that a lack of cointegration is neither necessary nor sufficient for the efficient market hypothesis to hold and that once market efficiency is defined as the lack of arbitrage opportunities there is no equivalence between market efficiency and cointegration.

References

1. Ammer, J. and J. Mei, 1996, "Measuring International Economic Linkages with Stock MarketData", Journal of Finance 51: 1743-1764.
2. Arshanapali, B. and J. Doukas, 1993, "International Stock Market Linkages: Evidence from the Pre- and Post-October 1987 Period", Journal of Banking and Finance 17: 193-208.
3. Banerjee, A., R. Lumsdaine and J. Stock, 1992, "Recursive and Sequential Tests of the Unit-Root and Trend-Break Hypothesis: Theory and International Evidence", Journal of Business & Economic Statistics 10: 271-287.
4. Caporale, G. and N. Pittis, 1998, "Cointegration and Predictability of Asset Prices", Journal of International Money and Finance 17: 441-453.
5. Dwyer, G. and M. Wallace, 1992, "Cointegration and Market Efficiency", Journal of International Money and Finance 11: 318-327.
6. Fernández-Serrano, J. L. and R. Peruga, 1999a, "Un Contraste ADF Secuencial para la Detección de Cambios en la Tendencia Estocástica", Working Paper 5/99, Universidad Europea-CEES.
7. Fernández-Serrano, J. L. and R. Peruga, 1999b, "Un Contraste ADF Secuencial para la Detección de Cambios en el Orden de Integración", Working Paper 6/99, Universidad Europea-CEES.
8. Engle, R.F. and C.W.J. Granger, 1987, "Cointegration and Error Correction: Representation, Estimation and Testing", Econometrica 55: 251-256.
9. Gregory, A.W. and B.E. Hansen, 1996, "Residual-Based Tests for Cointegration in Models with Regime Shifts", Journal of Econometrics 70: 99-126.
10. Janakiramanan, S. and A. S. Lamba, 1998, "An Empirical Examination of Linkages between Pacific-Basin Stock Markets", Journal of International Financial Markets 8: 155-173.
11. Karolyi, A. and R. M. Stulz, 1996, "Why Do Markets Move Together? An Investigation of US-Japan Stock Return Co-movements", Journal of Finance 51: 951-986.
12. King, A. M. and Wadhwani, S., 1990, "Transmission of volatility between stok markets", Review of Financial Studies 3: 5-33.
13. Koch, D. P. and T. W. Koch, 1991, "Evolution in Dynamic Linkages across Daily National Stock Indexes", Journal of International Money and Finance 10: 231-251.
14. Lin, S. M., Craft, K. and V. Chow, 1996, "Spectral Analysis in Three Dimensions: The Examination of Economic Interdependence between New York, London, Tokyo and the Pacific Basin Equity Market Indices", Journal of Applied Business Research 12: 72-84.
15. Montañés, A., 1996, "Contraste de Raíz Unitaria y Ruptura Estructural: Un Estudio de Monte Carlo para los Estadísticos Rolling, Recursivo y Secuencial", Revista Española de Economía 13, 39-74.
16. Perron, P. and T.J. Vogelsang, 1992, "Non-Stationarity and Level Shifts with an Application to Purchasing Power Parity", Journal of Business & Economic Statistics 10, 301-320.
17. Zivot, E. and D. Andrews, 1992, "Further Evidence on the Great Crash, the Oil Price Shock, and the Unit Root Hypothesis", Journal of Business & Economic Statistics 10, 251-270.

Table 1. Summary statistics

Table 2: Correlation coefficients between daily market returns

Table 3: Individual stock indices Panel A: Stability analysis of stochastic trend

Panel B: Analysis of the order of integration

Note: * and ** denotes significance at the 95% at 90% level, while ™ denotes marginal significativity.

Table 4: Difference with the Japanese index Panel A: Stability analysis of stochastic trend

Panel B: Order of partial integration

Note: * and ** denotes significance at the 95% at 90% level, while denotes marginal significativity.

Table 5: Cointegration tests National index = Japanese index Panel A: Whole sample

Panel B: Subsamples

Note: * and ** denotes significance at the 95% at 90% level, while denotes marginal significativity.

Critical values:

Changes in the stochastic trend

Change in the order of integration

Gregory and Hansen's test

Nikker 225 Stock Average Taiwan SE Weighted

Hang Seng - Nikkei 225 Stock Average

Figure 1. Levels of the indices together with Japanese index

Figure 2. Difference of the indices with Japanese Index

Korea SE Composite - Nikkei 225 Stock Average

COLECCION RESUMENES

98-01: "Negociación colectiva, rentabilidad bursátil y estructura de capital en España", Alejandro Inurrieta.

TEXTOS EXPRESS

99-02: "Economic implications of the demographic change in Spain: Call for research", Namkee Ahn.

99-01: "Efectos macroeconómicos de la finalización de las ayudas comunitarias", Simón Sosvilla-Rivero y José A. Herce.

DOCUMENTOS DE TRABAJO

2000-11: "Modelling evolving long-run relationships: The linkages between stock markets in Asia", José L. Fernández-Serrano y Simón Sosvilla-Rivero.

2000-10: "Integration and Inequality: Lesson from the Accessions of Portugal and Spain to the EU", Juan F. Jimeno, Olga Cantó, Ana Rute Cardoso, Mario Izquierdo y Carlos Farinha Rodrigues.

2000-09: "Explaining Youth Labor Market Problems in Spain: Crowding-Out, Institutions, or Technology Shifts", Juan J. Dolado, Florentino Felgueroso y Juan F. Jimeno.

2000-08: "Distributional aspects of the quality change bias in the CPI: Evidence from Spain", Javier Ruiz-Castillo, Eduardo Ley y Mario Izquierdo.

2000-07: "Testing chaotic dynamics vía Lyapunov exponents", Fernando Fernández-Rodríguez, Simón Sosvilla-Rivero y Julián Andrada-Félix.

2000-06: "Convergencia: Un análisis conjunto de los sectores. Aplicación al caso de las regiones españolas", Pablo Álvarez de Toledo, Jaime Rojo, Álvaro Toribio y Carlos Usabiaga.

2000-05: "The Laspeyres bias in the Spanish consumer price index", Javier Ruiz-Castillo, Eduardo Ley y Mario Izquierdo.

2000-04: "Evaluación de los efectos del Plan Prever a partir de un modelo de simulación de reemplazos del parque español de automóviles", Omar Licandro y Antonio R. Sampayo.

2000-03: "Minimum consumption, transitional dynamics and the Kuznets curve", María José Alvarez y Antonia Díaz.

2000-02: "Vintage human capital, demographic trends and endogenous growth", Raouf Boucekkine, David de la Croix y Omar Licandro.

2000-01: "Vintage capital and the dynamics of the AK model", Raouf Boucekkine, Omar Licandro, Luis A. Puch y Fernando del Río.

99-21: "Los efectos macroeconómicos de la Agenda 2000", Simón Sosvilla-Rivero y José A. Herce.

99-20: "Unemployment duration and workers' wage aspirations in Spain", Namkee Ahn y J. Ignacio García-Pérez.

99-19: "El patrón inversor de los establecimientos industriales de la Comunidad de Madrid", Ana Goicolea, Omar Licandro y Reyes Maroto.

99-18: "Crecimiento óptimo, depreciación endógena y subutilización del capital", Omar Licandro, Luis A. Puch y J. Ramón Ruiz Tamarit.

99-17: "Panel data and tourism demand. The case of Tenerife", F. J. Ledesma-Rodríguez, M. Navarro-Ibáñez y J. V. Pérez-Rodríguez.

99-16: "Redistribution in the Spanish pension system: An approach to its life time effects", Joan Gil y Guillem López-Casasnovas.