Causality in Volatility Between Developed and Emerging Equity ...

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Causality in Volatility Between Developed and Emerging Equity Markets: Analysis Based on the Markov Switching Heteroscedasticity Model

Ramaprasad Bhar School of Banking and Finance The University of New South Wales Sydney 2052, AUSTRALIA E-mail: [email protected] and Shigeyuki Hamori Faculty of Economics, Kobe University 2-1 Rokkodai, Nada-Ku Kobe, 657-8501 JAPAN E-mail: [email protected]

Abstract: This paper analyses the stock return characteristics for the two developed and several regional emerging markets using monthly return to capture the changes in mean-variance in a two state framework. An unobserved Markov process drives the evolution of the states. The approach allows both the mean and the variance to depend on the unobserved states and the model is estimated in one step. The propensity of any market to stay in a particular state is inferred from the estimated model parameters. The paper then extends the analysis by examining the causality in the volatility process between the two largest economies and the regional emerging markets using a recently developed procedure, which is robust to distributional assumptions. The economic intuitions behind the observations are also explored. JEL classification number: G15 Key words: Markov switching heteroscedasticity model, emerging market, volatility spillover, cross-correlation.

Please send correspondence to: Shigeyuki Hamori Faculty of Economics, Kobe University 2-1, Rokkodai, Nada-Ku, Kobe, 657-8501 JAPAN Email: [email protected]

Causality in Volatility Between Developed and Emerging Equity Markets: Analysis Based on the Markov Switching Heteroscedasticity Model

Abstract: This paper analyses the stock return characteristics for the two developed and several regional emerging markets using monthly return to capture the changes in mean-variance in a two state framework. An unobserved Markov process drives the evolution of the states. The approach allows both the mean and the variance to depend on the unobserved states and the model is estimated in one step. The propensity of any market to stay in a particular state is inferred from the estimated model parameters. The paper then extends the analysis by examining the causality in the volatility process between the two largest economies and the regional emerging markets using a recently developed procedure, which is robust to distributional assumptions. The economic intuitions behind the observations are also explored. JEL classification number: G15 Key words: Markov switching heteroscedasticity model, emerging market, volatility spillover, cross-correlation.

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1. Introduction The stock market volatility has been a widely studied area of research in financial economics. Shiller (1993) presents a number of research articles documenting the sources of market volatility. It has been suggested there that it is important for investors to understand the underlying reasons so that actions can be taken that will reduce their impact. Shiller defines excess volatility is the part that is in addition to that can be justified by efficient market hypothesis and explores some popular models in order to understand the events surrounding the stock market crash in October 1987. High levels of volatility have not only been recorded during such isolated events, Jochum (1999) reports regular occurrences of such events for Swiss market. Much research efforts have also been directed toward modelling market volatilities. It has important implications on the derivatives markets as well. Volatility models based on autoregressive conditional heteroscedasticity (ARCH) have been particularly successful in capturing some of the stylised facts. GARCH (generalized ARCH) models have been used by researchers to account for leptokurtosis, skewness and volatility clustering often characterising stock returns. Nelson (1991) and Glosten, Jagannathan and Runkle (1993) extend the standard GARCH model to take into account of the fact that negative shocks in the past period affect the conditional volatility differently compared to positive shocks in the past period. Bollerslev, Chou and Kroner (1992) suggest that although GARCH effects may be highly significant with many daily and weekly financial data, its effect tends to be much milder in less frequently sampled data e.g. quarterly data. The presence of sequential structural shifts due to the nature of news releases in the market, as a cause of conditional heteroscedasticity, has also been proposed by other researchers e.g. Kim and Kon (1996, 1999). In this context, the stock market returns may be viewed as drawn from a mixture of normal distributions. As a rationale for different regimes in the stock market, Ceccehetti, Lam and Mark (1990) propose that this may be due to the switching of the economy’s endowment between high and low growth phases. More recently, Kim, Nelson and Startz (1998) adopt Markov switching heteroscedasticity as the alternative way of dealing with ARCH effects in economic data. The main difference between the ARCH type conditional heteroscedasticity and Markov switching variance model is that in case of the former the unconditional variance is constant

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whereas for the latter it is changing depending on the state the economy is in. If there are sequential changes in regime, as suggested by some authors, then it may be more intuitive to think in terms of different regimes contributing to the return generating process in the stock market. Hamilton and Susmel (1994) also suggest that the long-run variance dynamics may be subjected to regime shift but within a regime it may be following an ARCH type process. Using weekly data Hamilton and Susmel show that the ARCH effect completely dies out after a month. It, therefore, makes sense to analyse less frequently sampled data (e.g. monthly) in a Markov switching heteroscedasticity framework. In the Markov switching framework Chu, Santoni and Liu (1996) adopt a two-stage process to describe the return behaviour in the stock market. They model the stock return as a Markov switching process in the first stage. In the second stage they estimate a volatility equation given different return regimes derived from the first stage. They find evidence of higher volatilities when the returns are either above or below some “normal” level. They also found that the increase in volatility is larger for negative deviations in returns than for positive deviations. This leads them to conclude that the return and volatility are non-linearly related and the relationship is asymmetric. Although many of the cited articles earlier use U.S. data for empirical analysis, in a recent paper, Cha and Oh (2000) explore the relationship between developed equity markets and the emerging equity markets in the Pacific Basin. They adopt the vector autoregression framework to analyse the influence of the U.S. and the Japanese markets on equity markets of Hong Kong, Korea, Singapore and Taiwan. In this paper we adopt the Markov switching heteroscedasticity model to characterise the return behaviour of several equity markets, both developed and emerging, using monthly data. Our approach differs from that of Chu et al (1996) in the sense that we allow both mean and variance to depend on the unobserved state and estimate them in one step. We focus on the regional characteristics and examine the relationship between Japan and three Asian markets e.g. India, Korea and Philippines and the U.S. and four South American markets e.g. Brazil, Chile, Columbia and Venezuela. In the first phase, we model the mean-variance return characteristics in a two state framework, where an unobserved Markov process drives the states. This allows us to estimate the variance process for each of the markets as well as to make inferences about the probability of a market staying in a particular volatility state given that it is already in that state. 4

In the second phase we extend the analysis by examining the causality in the volatility process between Japan and three other Asian markets and between U.S.A. and four other South American markets, using a recently developed method that is robust to distributional assumption. The importance of examining causality in volatility lies in the fact that this reflects the impact of information arriving in the market and how the market participants utilise this. In this context, the analysis presented here is likely to reveal the dominant regional source of information causing changes in the other markets. The method developed by Cheung and Ng (1996) relies on analysing cross-correlation function of the standardised residuals from the univariate models of a pair of series under consideration. It does not depend on simultaneous modelling of the inter- and intra- variable dynamics. Adequacy of each univariate model may, however, be established with the help of portmanteau statistics computed from the standardised residual as well as from the squared standardised residual. Since simultaneous modelling is not required in order to study causality, this method is suitable for dealing with relatively large number of series. Besides the test statistic has a well-defined asymptotic distribution. The plan of the paper is as follows. In the next section we discuss the model we adopt to analyse the monthly data. We then describe the data set used in this study. This is followed by the analysis of the empirical results. The last section contains some concluding remarks.

1. The Proposed Model As our preliminary investigation into the time series properties of the stock return series indicate, we model the series as an AR (1) process with mean and variance depending on an unobserved state. Denoting the return at time t by yt, the two-state Markov meanvariance model may be written as,

(y

t

)

(

)

− µ St = φ1 y t −1 − µ St −1 + ε t ,

(

ε t ~ i.i.d.N 0, σ St

2

)

(1)

where,

Pr.[St = j | St = i ] = pij ,

i, j = 1,2,

2

∑p j =1

ij

= 1,

(2)

µSt = µ1S1t + µ 2S2t ,

(3)

σS2t = σ12S1t + σ22S2t , and

(4)

5

Smt = 1, if St = m, and Smt = 0 otherwise .

Constructing the probability weighted likelihood function and maximising this with respect to the model parameters carry out the estimation of the model. In this context we follow the procedure discussed in Kim and Nelson (1999, page 65) to deal with the unobserved state variable. The estimation process also yields the filtered probabilities i.e. the probabilities pij about the state St conditional on the information, Ψ t , up to time. The estimate of the smoothed probabilities about the state conditional on all the information in the sample, Ψ T , is obtained by following the algorithm described in Kim and Nelson (1999, page 68). Given the estimates of the parameters and the smoothed probabilities, it is then straightforward to compute the variance of the stock returns as follows: E(σ2t | Ψ T ) = σˆ 12 E[St = 1| Ψ T ] + σˆ 22E[St = 2 | Ψ T ]

(5)

where, σˆ 12 is the estimate of volatility is state 1, σˆ 22 is the estimate of the volatility in state 2,

Ψ T is the complete observation set. Besides, we perform the model diagnostics using the residual generated during the construction of the likelihood function. This may be described as, y t − E [ y t | Ψ t −1 ] = y t − E µSt | Ψ t  − φ1E  y t −1 − µSt −1 | Ψ t  .

(6)

The above expression may be interpreted as the forecast error. The standardised residuals are generated with the help of equations (5) and (6). These are used to carry out the model diagnostics and form the basis of Cheung and Ng (1996) measure of pair wise causality tests. They show that under the no-causality hypothesis, the cross correlation at different lags are not significantly different from zero and the statistic T ϒ1,2 (k) is asymptotically normally distributed, where ϒ1,2 (k) is the cross correlation between the series 1 and 2 at lag k. Cheung and Ng show that this result is robust to distributional assumptions. The causality in mean is tested using standardised residuals and the causality in variance is tested using squared standardised residuals.

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2. Data Used

This paper uses the data on the monthly stock prices in Japan and Asian-Pacific group, i.e., Japan, India, Korea, and Philippines, and USA and Latin America group, i.e., USA, Brazil, Chile, Columbia, and Venezuela. The source is the International Financial Statistics of the International Monetary Fund. The sample period is January 1980 through March 1999. The rate of return is calculated as follows:

yt =

Pt − Pt −1 × 100 Pt −1

where Pt is the stock priced index at time t. Thus, stock returns are obtained for the period between February 1970 and March 1999. Table 1 shows the summary statistics on stock return in each country. This table displays the mean, standard deviation (Std. Dev.), skewness, kurtosis, and the p-value of the Jarque-Bera test (JB test). The hypothesis of normal distribution may not be rejected at the 5% (1%) level of significance if the p-value for the JB-test is greater than 0.05 (0.01). Table 2 shows the correlation among stock returns of each country. It is clear from Table 1, the average return of Korea, India and Philippine is higher than that of Japan, whereas the standard deviation of return of Korea, India and Philippine is larger than that of Japan. Similarly, the average return of Brazil, Chile, Columbia, and Venezuela is higher than that of USA, whereas the standard deviation of return of Brazil, Chile, Columbia, and Venezuela is larger than that of USA. Thus, it is found that the markets in emerging countries are higher risk and higher return than the markets of developed countries in the same region. The hypothesis of normal distribution is to be rejected at the 1% significance level for all countries except Japan.

3. Empirical Results

Table 3 shows the empirical results of Markov switching heteroscedasticity estimation for Japan and the Asia-Pacific markets. The estimates of transition probability p11 (low-

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variance state) are all statistically significant at the 1% level. The estimates of transition probability p 22 (high-variance state), although not significant for all, are much smaller in magnitude compared to p11 . The estimates of variance in the low-volatility state are all statistically significant and ranges from a low of 6.97 (Japan) to a high of 47.94 (Philippines). The estimates of variance in the high-volatility state are also all statistically significant and ranges from 24.51 (Japan) to 1710.34 (Philippines). Although the variance in the high-volatility state is several times higher than the variance in the low-volatility state, it is particularly so for Philippines. Focusing on the mean return, we find that the mean in the low-volatility state is significant for Japan and India whereas for the high-volatility state it is significant for Korea and the Philippines. Table 4 gives the diagnostics of the empirical results for Japan and the Asia-Pacific markets. It is clear from the table that the null hypothesis of no autocorrelation (in both the standardised residual and the squared standardised residual) is not rejected for Japan, India and the Philippines at conventional level of significance. For Korea LB2(16) test is not significant. The null hypothesis of normality is not rejected for all countries except Philippines at the 1% significance level. Overall conclusion from these diagnostic tests is that the Markov switching heteroscedasticity model describes the data generating process for these markets quite well. Table 5 displays the empirical results of Markov switching heteroscedasticity estimation for USA and Latin America markets. The estimates of transition probability p11 (low-variance state) are all statistically significant and of similar magnitude as in the case Japan and Asia-Pacific markets. The estimates of probability p 22 (high-variance state) are also significant except for Brazil and Chile. The variance in the low-volatility state ranges from a low of 4.81 (Venezuela) to a high of 167.24 (Brazil) and all estimates are statistically significant. The variance in the highvolatility state ranges from 38.86 (U.S.A.) to 1043.09 (Columbia). They are significant at the 1% level for all countries. Although the variance in the high-volatility state is several times higher than the variance in the low-volatility state for all the countries, it is particularly so for Venezuela. The magnitude of the variance in the-volatility state is minimum for the U.S.A. The mean return in the low volatility state is statistically significant for the U.S.A., Brazil and Columbia, whereas it is significant in the high-volatility state for Brazil, Chile and Venezuela.

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Table 6 gives the diagnostics of the empirical results for USA and Latin American markets. It is clear from the table that the null hypothesis of no autocorrelation in the standardised residual is not rejected for all the markets in this group. The result is similar for the squared standardised residual except for Venezuela. The null hypothesis of normality is not rejected for all countries except Venezuela at the 1% significance level. Overall conclusion from these diagnostic tests is that the Markov switching heteroscedasticity model fits the return data from these group of countries very well. Tables 3, 4, 5, and 6 help us make some interesting observations about the similarity and differences between the developed and the emerging markets in different regions. The first point is about the estimated probability of staying in the same state for these markets. Tables 3 and 5 indicate that the probability ( p11 ) of staying in regime 1 i.e. the low-volatility state is very high. On the other hand, the regime 2 (the large-volatility state) is relatively unstable. Thus, if the current month falls inside the low-variance state, then the probability of returning to the same state next month is very high. These characteristics are common to both the developed markets and the developing markets. It is interesting to note that only the U.S.A. has the maximum propensity to stay in the high volatility state once it is already in that state. The second point is about the differences in the magnitude of the variance in different regimes. The variance in the high-volatility state is several times higher than the variance in the low-volatility state for all the countries. This characteristic is particularly evident for emerging markets. Thirdly, the developed countries have higher return in the lowvolatility state. This is consistent with Chu et al (1996). On the other hand, emerging countries have lower return in low volatility state. Thus, risk-return relationship is different between developed countries and emerging countries. Finally, it is clear from the diagnostics of the model (Tables 4 and 6) that the model fits better the developed markets than the emerging markets, although the overall fitting of the model is good. Figures 1 through 9 plot the computed variance series for each country [See equation (5).]. The movements of variance differ from country to country. For example, Korea and Philippines experience relatively intense change, whereas Japan and India experience relatively mild change. It can be seen from the figures, however, that there are two periods when the variance moves together internationally. One corresponds to the Black Monday that occurred in 1987 and the other is the crash of the Japanese stock market that occurred in 1990. These are typically observed in India. There are two peaks in India variance series, which correspond to these two incidents. A high variance continued only for Japan in the 9

1990s. A possible explanation is the collapse of bubbles in the stock market. This caused an increased in uncertainty in the Japanese economy in the 1990s and thus increased its variance. Philippines and Korea also experience large movement in variance in 1997, which corresponds to the Asian currency crisis. The figures also depict the co-movement of variances of USA and four Latin America markets. The movements of variance differ from country to country and there is no definite pattern emerging. For example, Chile, USA, and Venezuela experience relatively intense change, whereas Brazil and Columbia experience relatively mild change. It is clear from figures, however, there are two periods that variance moves together internationally. One corresponds to the period of default problem in southern American countries which occurred around 1982, and the other corresponds to the Black Monday occurred in 1987. The mild change in variance after 1995 in Brazil and Columbia might reflect the recovery of economic situation for both countries. Table 7 and Table 8 show the empirical results of the bivariate causality test for mean and variance series using the procedure developed by Cheung and Ng (1994). In Table 7, cross correlation-based analysis of causality between Japan and Asian countries are reported, whereas in Table 8 cross correlation-based analysis of causality between the US and Latin American countries are reported. In Tables 7 and 8, lags are measured in months, and negative lag implies lead. In Table 7, for an example, lag refers to the number of months that Japan causes Asian countries, whereas lead refers to the number of months that Asian countries cause Japan. The upper half and the lower half of each table respectively shows the causality in mean and the causality in variance. The cross correlation function (CCF) of standardized residuals is used to test the null hypothesis of no-causality in mean, whereas the CCF of squared-standardized residuals is used to test the null hypothesis of no-causality in variance.

Under the null hypothesis of no-causality, the cross correlation at different lags

are independently and normally distributed in large samples. That is, there is no evidence of causality in mean (in variance) when all the cross correlation coefficients calculated from (squares of) standardized residuals, at all possible leads and lags, are not significantly different from zero. The causality pattern is indicated by significant cross correlation. In Table 7, the cross correlation at lag 0 (contemporaneous correlation) is –1.10 (India), 3.15 (Korea), and 2.13 (Philippines) for causality in mean, and they are statistically significant at the 5% level except India. The cross correlation at lag 0 is –0.14 (India), -0.84

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(Korea), and –0.54 (Philippines) for the causality in variance, but none of them are statistically significant at the 5% level. We can see some interesting characteristics from the empirical results of causality test. Japan causes India only in mean, whereas India causes Japan neither in mean nor variance. Japan causes Korea only in mean, whereas Korea causes Japan both in mean and in variance. This is indicative of similarity of industrial structure of Japan and Korea. There is causal relation between Japan and Philippines only in mean. It is interesting to see that the causal relation between Japan and Asian countries is relatively strong in mean, but not in variance. The results are summarized in Figure 10. In Table 8, the cross correlation at lag 0 (contemporaneous correlation) is 1.98 (Brazil), 2.12 (Chile), 1.12 (Columbia), and 1.99 (Venezuela) for causality in mean, and they are statistically significant at the 5% level except Columbia. The cross correlation at lag 0 is 1.16 (Brazil), 4.05 (Chile), -0.18 (Columbia), and 2.38 (Venezuela) for the causality in variance, and they are statistically significant at the 5% level for Chile and Venezuela. The main hypothesis being examined is that importance of USA in causing volatility in emerging Latin American economies. Judging from this table, we can see that the USA causes Brazil and Venezuela in mean, and Columbia causes the USA in mean. At the same time, the USA causes Chile and Columbia in variance, whereas Columbia and Venezuela cause the USA in variance. It is interesting to see that Columbia causes the USA both in mean and in variance. The results are summarized in Figure 11.

4. Concluding Remarks

This paper analyses the stock return characteristics for the two developed and seven emerging countries in two different regions using monthly return and captures the changes in mean-variance in a two state framework, where an unobserved Markov process drives the states. This paper allows both the mean and variance to depend on the state and estimate the model in one step. The paper also extends the analysis by examining the causality in the volatility process and examining the economic intuition behind the results. The residual diagnostics clearly establish the appropriateness of the Markov Switching heteroscedasticity model of stock return. It is found that the low volatility state is relatively stable, whereas the large volatility state is relatively unstable. Thus, if the current month falls inside the low-variance state, then the probability of returning to the same state 11

next month is very high. It is also interesting to note that of the two developed markets, the U.S.A has a very high propensity to stay in the high volatility state once it is already in that state. The paper also computes the variance series for all the nine countries based on the estimated model parameters and finds that there are two periods when the variance moves together internationally.

For the Japan and the Asian emerging countries this typically

corresponds to the Black Monday of October 1987 and the other one is the crash of the Japanese stock market in 1990. The estimates of India depict this clearly. On the other hand, for the U.S.A. and the southern American countries this corresponds to the default problem in 1982 and again in October 1987. The mild change in variance after 1995 for Brazil and Columbia might reflect the recovery of economic situation for both these countries. The Cheung and Ng (1996) procedure, which is robust to distributional assumption, is used to test for causality in both mean and variance. The observed causation show some interesting results. There is causal relation between developed countries and developing countries at least either in mean or in variance. Thus, The information flows between stock markets affect not only price movements but also volatility movements in the world. Our results show that information flows between the US (or Japan) and other stock markets in the region can be reflected in both price and volatility spillovers.

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Appendix

The stock price indices are obtained from the International Financial Statistics of the International Monetary Fund. The series code of stock price index in each country is shown as follows: Japan: 15862...ZF India: 53462...ZF... Korea: 54262...ZF... Philippines: 56662...ZF... USA: 11162...ZF Brazil: 22362...ZF... Chile: 22862...ZF... Columbia: 23362...ZF... Venezuela: 29962...ZF...

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References

Bollerslev, T. Chou, R. Y and Kroner, K. F., 1992, ARCH modelling in finance: A review of the theory and empirical evidence, Journal of Econometrics, 52, 5-39. Cecchetti, S. G., Lam, P. S. and Mark, N. C., 1990, Mean reversion in equilibrium asset prices, American Economic Review, 80, 398-418. Cha, B. and Oh, S., 2000, The relationship between developed equity markets and the Pacific Basin’s emerging equity markets, International Review of Economics and Finance, 9, 299-322. Cheung, Y-W. and Ng, L. K. (1996), A Causality-in-Variance test and Its Application to financial Market Prices, Journal of Econometrics, 72, 33-48. Chu, C. J., Santoni, G. J. and Liu, T., 1996, Stock market volatility and regime shifts in returns, Information Sciences, 94, 179-190. Glosten, L. R., Jagannathan R. and Runkle D.E., 1993, On the relation between the expected value of and the volatility of nominal excess return on stocks, Journal of Finance 53, 1779-1801. Hamilton, J. D. and Susmel, R. (1994), Autoregressive Conditional Heteroscedasticity and Changes in Regime, Journal of Econometrics, 64, 307-333. Hamori S. and Imamura Y., 2000, International transmission of stock prices among G7 countries: LA-VAR approach, Applied Economics Letters, 7, 613-618. Jochum, C., 1999, Volatility spillovers and the price of risk: Evidence from the Swiss stock market, Empirical Economics, 24, 303-322. Kim, C-J. and Nelson, C. R. 1999, State-Space Models with Regime Switching, Classical and Gibbs Sampling Approaches with Applications, The MIT Press, Cambridge, Massachusetts. Kim, C-J., Nelson, C. R. and Startz, R. 1998, Testing For Mean Reversion In Heteroscedastic Data Based On Gibbs Sampling Augmented Randomisation, Journal of Empirical Finance, 5, 131-154. Kim, D., and Kon, S. J., 1996, Sequential parameter nonstationarity in stock market returns, Review of Quantitative Finance and Accounting, 6, 103-131. Kim, D., and Kon, S. J., 1999, Structural change and time dependence in models of stock returns, Journal of Empirical Finance, 6, 283-308. Nelson, D. B., 1991, Conditional heteroskedasticity in asset returns: a new approach, Econometrica, 59, 347-370. 14

Shiller, R. J., 1993, Market volatility, The MIT Press, Cambridge, Massachusetts.

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Mean Std. Dev. Skewness Kurtosis JB Test

Table 1 Summary Statistics Japan and Asia-Pacific Markets India Japan Korea 1.2549 0.5120 0.9831 6.3806 4.4012 6.6701 0.7466 -0.0774 0.2626 7.4358 3.6302 4.2551 0.0000 0.1330 0.0001

Mean Std. Dev. Skewness Kurtosis JB Test

USA and Latin America Markets Chile Columbia 2.0668 1.6477 6.9328 11.8359 0.5338 0.2034 3.3181 33.6014 0.0026 0.0000

Brazil 15.7945 26.3562 0.8869 4.2961 0.0000

USA 1.1590 3.4889 -0.4886 5.7595 0.0000

Philippine 1.9628 18.3355 4.9224 44.8036 0.0000

Venezuela 2.1801 13.7816 0.4680 9.1551 0.0000

The hypothesis of normal distribution may not be rejected at the 5% (1%) significance level if the p-value for the JB-test is greater than 0.05 (0.01).

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India Japan Korea Philippines

Brazil Chile Columbia USA Venezuela

Table 2 Correlation of Stock Returns Japan and Asia-Pacific Markets India Japan Korea 1.0000 -0.1142 0.0761 -0.1142 1.0000 0.3110 0.0761 0.3110 1.0000 0.0958 0.1136 0.1626

Brazil 1.0000 0.1330 0.0587 0.0787 0.0218

USA and Latin America Markets Chile Columbia 0.1330 0.0587 1.0000 0.0177 0.0177 1.0000 0.1598 0.0703 -0.0050 0.0921

USA 0.0787 0.1598 0.0703 1.0000 0.0491

Philippine 0.0958 0.1136 0.1626 1.0000

Venezuela 0.0218 -0.0050 0.0921 0.0491 1.0000

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Table 3 Parameter Estimates: Markov Switching Heteroscedasticity Model of Stock Return Japan and Asia-Pacific Markets Japan India Korea Philippines p11 p 22 σ12

0.9771***

0.9839***

0.9419***

0.9344***

(0.0206)

(0.0136)

(0.0333)

(0.0494)

0.0169

0.2244

*

0.0701

0.3609*

(0.0158)

(0.1618)

(0.0430)

(0.1871)

***

6.9704

(1.2401)

σ22 µ1

***

24.5091

φ1

21.5985

(2.6211)

***

14.6857

(3.9624) **

238.0011

***

68.0836

47.9405*** (16.7452)

1710.3386***

(3.3390)

(122.2484)

(14.0668)

(622.5834)

***

***

1.252

-0.0711

-0.3935

(0.3339)

(0.4084)

(0.5774)

0.2425

1.9803

*

2.3073

14.7534*

(0.4586)

(4.2063)

(1.0166)

(8.6261)

(0.3186)

µ2

***

***

0.2911

(0.0646)

1.1089

***

0.3628

(0.0638)

***

0.2441

(0.0705)

0.0060 (0.0584)

The parameters are described in text. Standard errors are given in parentheses below the parameter estimates. Significance at the 1% level is indicated by *** , at the 5% level is indicated by **, and at the 10% level by *.

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Table 4 Diagnostics Using Standardised Residual From Markov Switching Heteroscedasticity Model Japan and Asia-Pacific Markets Japan India Korea Philippines LB (16) LB2 (16) JB-Test

0.315 0.247 0.625

0.201 0.181 0.458

0.541 0.001 0.606

0.010 0.999 0.001

LB (16) and LB2 (16) are the Ljung-Box tests of order 16 using standardised residuals and squared standardised residuals respectively. The JB-test is for normality obtained from Jarque-Bera statistic. Entries represent corresponding p-values. For LB (16) test, p-value greater than 0.05 (0.01) implies that the hypothesis of white noise cannot be rejected at the 5% (1%) level of significance. Similarly, for LB2 (16) remaining ARCH effect may be rejected for p-value greater than 0.05 (0.01) at the 5% (1%) level of significance. The hypothesis of normal distribution may not be rejected at the 5% (1%) level of significance if the p-value for the JB-test is greater than 0.05 (0.01).

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Table 5 Parameter Estimates: Markov Switching Heteroscedasticity Model of Stock Return USA and Latin American Markets USA Brazil Chile Columbia Venezuela p11 p 22

0.8492***

0.9804***

0.8919***

0.9626***

0.8883***

(0.0682)

(0.0157)

(0.0521)

(0.0214)

(0.0429)

***

0.7374

(0.1956)

σ

2 1

***

5.4783

(0.8123)

σ

2 2

***

38.8578

(13.5681)

µ1

***

1.2178

(0.1981)

µ2

0.5398 (1.1459)

φ1

***

0.2534

(0.0542)

0.0241

0.0463

(0.0162) ***

167.2423

(25.6942) ***

876.7970

(114.8868) **

2.8172

(1.3287) ***

27.9173

(3.5628)

-0.0152 (0.0644)

(0.0285) ***

8.1071

(1.9250) ***

52.9701

**

0.3120

(0.1385)

(0.0347)

***

28.8894

(4.4205)

1043.0854

(366.7880)

-0.0256

**

***

2.3963

(0.6270) ***

0.3697

(0.0616)

4.8088*** (1.0329)

***

(6.7705) (0.1657)

0.0748**

0.8279

308.9152*** (41.1411)

0.0566

(0.4181)

(0.2200)

7.3533

3.4216**

(6.7237)

(1.5228)

***

0.2324

(0.0638)

0.1027 (0.0721)

The parameters are described in text. Standard errors are given in parentheses below the parameter estimates. Significance at the 1% level is indicated by *** , at the 5% level by **, and at the 10% level is indicated by *.

20

Table 6 Diagnostics Using Standardised Residual From Markov Switching Heteroscedasticity Model USA and Latin American Markets USA Brazil Chile Columbia Venezuela LB (16) LB2 (16) JB-Test

0.782 0.222 0.031

0.524 0.011 0.714

0.241 0.297 0.274

0.358 0.994 0.030

0.491 0.002 0.001

LB (16) and LB2 (16) are the Ljung-Box tests of order 16 using standardised residuals and squared standardised residuals respectively. The JB-test is for normality obtained from Jarque-Bera statistic. Entries represent corresponding p-values. For LB (16) test, p-value greater than 0.05 (0.01) implies that the hypothesis of white noise cannot be rejected at the 5% (1%) level of significance. Similarly, for LB2 (16) remaining ARCH effect may be rejected for p-value greater than 0.05 (0.01) at the 5% (1%) level of significance. The hypothesis of normal distribution may not be rejected at the 5% (1%) level of significance if the p-value for the JB-test is greater than 0.05 (0.01).

21

Table 7 Cross Correlation Based Analysis of Causality Between Japan and Others Causality in Mean Lag

India

Korea

Philippines

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

0.32 0.17 1.45 0.76 0.88 -0.99 -1.10 0.06 1.92* -1.33 -1.10 -2.08* 1.05

-0.58 0.25 1.04 -0.47 -0.70 1.64* 3.15* 2.93* 0.99 -0.52 1.69* 1.38 -0.24

-0.40 -0.90 3.17* -0.12 -1.65* 2.12* 2.13* -1.21 -0.18 2.53* 0.75 -0.46 -0.26

Lag

India

Korea

Philippines

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

0.75 -0.67 1.14 -0.77 -1.45 -0.38 -0.14 1.11 -0.39 0.35 -0.26 0.55 0.82

-0.46 0.20 -0.22 -0.18 2.35* 0.09 -0.84 1.63 -0.66 -0.08 -0.15 0.04 -0.17

-0.12 0.70 -0.37 -0.73 0.07 -0.23 -0.54 -0.80 1.54 0.28 -0.88 -0.06 -0.51

Causality in Variance

The entries in the table are the Cheung and Ng (1996) statistics based on cross-correlation function between Japan and each of the other three countries. Lags are measured in months and negative lag implies lead. Under the null hypothesis of no causality the statistic has standard normal distribution. Significance at 5% is indicated by *. Significance at positive lag length indicates Japan is causing either mean or variance in the other country. Similarly significance at negative lag implies the opposite.

22

Table 8 Cross Correlation Based Analysis of Causality Between USA and Others Causality in Mean Lag

Brazil

Chile

Columbia

Venezuela

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

-0.47 -2.37* 0.35 -0.50 -0.43 -0.65 1.98* 0.22 -2.15* -0.11 -2.40* -0.40 -2.64*

-0.41 1.10 -0.78 -0.87 -1.18 0.50 2.12* 1.04 -0.32 -1.25 0.60 0.41 0.02

-0.39 1.06 -0.30 0.75 0.12 -2.09* 1.12 -0.01 -0.62 -1.32 -1.18 -0.45 0.75

-0.52 0.32 -0.35 0.32 -0.64 0.44 1.99* 0.65 -1.91* 0.05 0.92 -1.52 0.28

Lag

Brazil

Chile

Columbia

Venezuela

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

-0.16 0.33 1.33 0.77 -0.25 -0.66 1.16 0.55 -0.32 0.31 0.90 0.91 -0.13

0.77 0.87 0.44 1.54 0.26 1.53 4.05* -1.25 1.72* 1.91* 1.04 -0.86 -1.10

-0.04 1.75* -0.85 -0.27 -0.76 0.79 -0.18 0.82 -2.16* 0.21 -1.69* -0.86 0.61

-0.39 -0.74 -1.76* -1.00 -0.37 -0.16 2.38* -0.27 0.24 0.35 -0.02 -0.25 1.12

Causality in Variance

The entries in the table are the Cheung and Ng (1996) statistics based on cross-correlation function between USA and each of the other four countries. Lags are measured in months and negative lag implies lead. Under the null hypothesis of no causality the statistic has standard normal distribution. Significance at 5% is indicated by *. Significance at positive lag length indicates USA is causing either mean or variance in the other country. Similarly significance at negative lag implies the opposite.

23

Variance 30.00

25.00

20.00

15.00

10.00

5.00

0.00 Mar-80 Sep-80 Mar-81 Sep-81 Mar-82 Sep-82 Mar-83 Sep-83 Mar-84 Sep-84 Mar-85 Sep-85 Mar-86 Sep-86

Mar-88 Sep-88 Mar-89 Year

Sep-89 Mar-90 Sep-90 Mar-91 Sep-91 Mar-92 Sep-92 Mar-93 Sep-93 Mar-94 Sep-94 Mar-95 Sep-95 Mar-96 Sep-96 Mar-97 Sep-97 Mar-98 Sep-98 Mar-99

Figure 1 Variance for Japan

Mar-87 Sep-87

24

Variance 250.00

200.00

150.00

100.00

50.00

0.00 Mar-80 Sep-80 Mar-81 Sep-81 Mar-82 Sep-82 Mar-83 Sep-83 Mar-84 Sep-84 Mar-85 Sep-85 Mar-86 Sep-86

Mar-88 Sep-88 Year

Mar-89 Sep-89 Mar-90 Sep-90 Mar-91 Sep-91 Mar-92 Sep-92 Mar-93 Sep-93 Mar-94 Sep-94 Mar-95 Sep-95 Mar-96 Sep-96 Mar-97 Sep-97 Mar-98 Sep-98 Mar-99

Figure 2 Variance for India

Mar-87 Sep-87

25

Variance 80.00

70.00

60.00

50.00

40.00

30.00

20.00

10.00

0.00 Mar-80 Sep-80 Mar-81 Sep-81 Mar-82 Sep-82 Mar-83 Sep-83 Mar-84 Sep-84 Mar-85 Sep-85 Mar-86 Sep-86

Mar-88 Sep-88 Mar-89 Year

Sep-89 Mar-90 Sep-90 Mar-91 Sep-91 Mar-92 Sep-92 Mar-93 Sep-93 Mar-94 Sep-94 Mar-95 Sep-95 Mar-96 Sep-96 Mar-97 Sep-97 Mar-98 Sep-98 Mar-99

Figure 3 Variance for Korea

Mar-87 Sep-87

26

Variance 1800.00

1600.00

1400.00

1200.00

1000.00

800.00

600.00

400.00

200.00

0.00 Mar-80 Sep-80 Mar-81 Sep-81 Mar-82 Sep-82 Mar-83 Sep-83 Mar-84 Sep-84 Mar-85 Sep-85

Mar-87 Sep-87 Mar-88 Sep-88 Year

Mar-89 Sep-89 Mar-90 Sep-90 Mar-91 Sep-91 Mar-92 Sep-92 Mar-93 Sep-93 Mar-94 Sep-94 Mar-95 Sep-95 Mar-96 Sep-96 Mar-97 Sep-97 Mar-98 Sep-98 Mar-99

Figure 4 Variance for Philippines

Mar-86 Sep-86

27

Variance 45.00

40.00

35.00

30.00

25.00

20.00

15.00

10.00

5.00

0.00 Mar-80 Sep-80 Mar-81 Sep-81 Mar-82 Sep-82 Mar-83 Sep-83 Mar-84 Sep-84 Mar-85 Sep-85 Mar-86 Sep-86

Mar-88 Sep-88 Mar-89 Year

Sep-89 Mar-90 Sep-90 Mar-91 Sep-91 Mar-92 Sep-92 Mar-93 Sep-93 Mar-94 Sep-94 Mar-95 Sep-95 Mar-96 Sep-96 Mar-97 Sep-97 Mar-98 Sep-98 Mar-99

Figure 5 Variance for USA

Mar-87 Sep-87

28

Variance 1000.00

900.00

800.00

700.00

600.00

500.00

400.00

300.00

200.00

100.00

0.00 Mar-80 Sep-80 Mar-81 Sep-81 Mar-82 Sep-82 Mar-83 Sep-83 Mar-84 Sep-84 Mar-85 Sep-85 Mar-86 Mar-87 Sep-87 Mar-88 Sep-88 Year

Mar-89 Sep-89 Mar-90 Sep-90 Mar-91 Sep-91 Mar-92 Sep-92 Mar-93 Sep-93 Mar-94 Sep-94 Mar-95 Sep-95 Mar-96 Sep-96 Mar-97 Sep-97 Mar-98 Sep-98 Mar-99

Figure 6 Variance for Brazil

Sep-86

29

Variance 60.00

50.00

40.00

30.00

20.00

10.00

0.00 Mar-80 Sep-80 Mar-81 Sep-81 Mar-82 Sep-82 Mar-83 Sep-83 Mar-84 Sep-84 Mar-85 Sep-85 Mar-86 Sep-86

Mar-88 Sep-88 Mar-89 Year

Sep-89 Mar-90 Sep-90 Mar-91 Sep-91 Mar-92 Sep-92 Mar-93 Sep-93 Mar-94 Sep-94 Mar-95 Sep-95 Mar-96 Sep-96 Mar-97 Sep-97 Mar-98 Sep-98 Mar-99

Figure 7 Variance for Chile

Mar-87 Sep-87

30

Variance 1200.00

1000.00

800.00

600.00

400.00

200.00

0.00 Mar-80 Sep-80 Mar-81 Sep-81 Mar-82 Sep-82 Mar-83 Sep-83 Mar-84 Sep-84 Mar-85 Sep-85

Mar-87 Sep-87 Mar-88 Sep-88 Year

Mar-89 Sep-89 Mar-90 Sep-90 Mar-91 Sep-91 Mar-92 Sep-92 Mar-93 Sep-93 Mar-94 Sep-94 Mar-95 Sep-95 Mar-96 Sep-96 Mar-97 Sep-97 Mar-98 Sep-98 Mar-99

Figure 8 Variance for Columbia

Mar-86 Sep-86

31

Variance 350.00

300.00

250.00

200.00

150.00

100.00

50.00

0.00 Mar-80 Sep-80 Mar-81 Sep-81 Mar-82 Sep-82 Mar-83 Sep-83 Mar-84 Sep-84 Mar-85 Sep-85

Mar-87 Sep-87 Mar-88 Sep-88 Year

Mar-89 Sep-89 Mar-90 Sep-90 Mar-91 Sep-91 Mar-92 Sep-92 Mar-93 Sep-93 Mar-94 Sep-94 Mar-95 Sep-95 Mar-96 Sep-96 Mar-97 Sep-97 Mar-98 Sep-98 Mar-99

Figure 9 Variance for Venezuela

Mar-86 Sep-86

32

Figure 10 Causality Pattern between Japan and Other Countries Mean

India

J A Korea

P A

Philippines

N

Variance

J A

Korea

P A N

33

Figure 11 Causality Pattern between the USA and Other Countries Mean Brazil

U S

Columbia

A Venezuela

Variance

Chile

U S

Columbia

A Venezuela

34