This study analyzes the causal interlinkages in the stock markets of advanced emerging European and Asian economies using Hong’s [1] causality tests. Our empirical results provide evidence that direct and contemporaneous casual linkages among markets are weak. However, when we examine the indirect causal linkages, we find a significant return spillover effect in some cases.
The study related to causal interlinkages among various stock markets around the globe is crucial for institutional investors, hedge fund managers, portfolio managers and regulators. The emerging markets exhibit higher volatility and have plenty of opportunities for various market participants to make extraordinary gains in comparison to the opportunities available in the developed markets. In this paper, our interest is to investigate causal linkages among advanced emerging European and Asian markets (Czech Republic, Hungary, Poland, Turkey, Malaysia and Taiwan (China)).
Among the given advanced emerging European economies, Turkey appears to be the largest economy based on the given market capitalization. If we include the Asian economies, then Taiwan (China) is the largest of all the markets under study based on the market capitalization in both the periods (December 2009 and May 2012). Of all the markets under study, only Malaysia has shown a
Market capitalization (in US$ million) | Percentage of GDP | Percentage of world capitalization | ||||
---|---|---|---|---|---|---|
May-2012 | Dec-2009 | May-2012 | Dec-2009 | May-2012 | Dec-2009 | |
Czech | 38,094.00 | 41,441.98 | 23.39 | 21.79 | 0.08 | 0.09 |
Hungary | 18,515.00 | 30,100.10 | 21.38 | 23.77 | 0.04 | 0.07 |
Poland | 140,170.00 | 150,641.00 | 40.25 | 34.99 | 0.30 | 0.33 |
Turkey | 224,383.00 | 227,321.90 | 40.85 | 36.99 | 0.48 | 0.50 |
Malaysia | 404,987.00 | 284,047.90 | 170.82 | 147.24 | 0.87 | 0.62 |
Taiwan (China) | 721,745.00 | 733,052.40 | 182.95 | 194.21 | 1.55 | 1.60 |
significant increase in its market capitalization as a percentage of world markets’ capitalization. Furthermore, Hungary and Taiwan (China) have shown a decrease in the values of market capitalization as a percentage of their GDP. This indicates that most of the markets under study have been adversely impacted by the recent European debt crisis.
The core aim of this paper is to investigate the causal interlinkages among the stock markets of advanced emerging European and Asian economies using a modified version of Cheung and Ng [
The remainder of this paper is organized as follows. Section 2 presents the literature review. Section 3 reports the methodology used. Section 4 provides details on the data used and discusses the preliminary analysis. Section 5 provides the empirical results with discussion and Section 6 concludes with a summary of our main findings.
Billio and Pelizzon [
The study of causal inter-linkages among different stock markets began with the pioneering work of Granger [
E { ( X t + 1 − μ x , t + 1 ) 2 | I t } ≠ E { ( X t + 1 − μ x , t + 1 ) 2 | J t } (1)
where It and Jt are the information sets defined as I t = { X t − j ; j ≥ 0 } and J t = { X t − j , Y t − j ; j ≥ 0 } .
In the first step, a univariate GARCH model is fitted to both the processes, X and Y, to separate out the standardized residuals to be used in the second step. As a preliminary step, we first compare the standard GARCH model and Markov regime switching GARCH model to identify the best model in terms of fitting the data well. In the second step, we estimate the cross-correlation function proposed by Hong [
Suppose pt is the value of a stock market index at time t. Then, the continuously compounded return rt is given as:
r t = ln ( p t p t − 1 )
The standard generalized autoregressive conditional heteroskedasticity (GARCH) model is given as:
r t = δ + ε t = δ + z t h t , ε t = z t h t , z t ~ N ( 0 , 1 )
h t = α 0 + α 1 ε t − 1 2 + β 1 h t − 1 (2)
where α 0 > 0 , α 1 ≥ 0 and β 1 ≥ 0 .
The general form of MRS-GARCH model is given as:
r t = μ t ( i ) + ε t = δ ( i ) + ε t , ε t ~ N ( 0 , h t )
h t ( i ) = α 0 ( i ) + α 1 ( i ) ε t − 1 2 + β 1 ( i ) h t − 1 (3)
where ht-1 is a state-independent average of past conditional variances and i = 1 and 2, the two states of the MRS-GARCH model which are indexed by an unobserved latent variable St and it takes the values 0 and 1as per the state of the markets. The variable St is assumed to follow a first-order Markov chain with a fixed transition probability matrix P given by:
P = [ p 11 p 21 p 12 p 22 ] = [ p 1 − q 1 − p q ] (4)
where p i j = Pr ( S t = j | S t − 1 = i ) for i = 0, 1. The ergodic probability to be in state St = 1 is written as:
π 1 = ( 1 − p ) ( 2 − p − q )
and the unconditional probability to be in state St = 0 is written as:
π 2 = 1 − π 1
Cai [
h t − 1 = E t − 2 { h t − 1 ( j ) } = p 1 , t − 1 [ ( μ t − 1 ( 1 ) ) 2 + h t − 1 ( 1 ) ] + ( 1 − p 1 , t − 1 ) [ ( μ t − 1 ( 2 ) ) 2 + h t − 1 ( 2 ) ] − [ p 1 , t − 1 μ t − 1 ( 1 ) + ( 1 − p 1 , t − 1 μ t − 1 ( 2 ) ) ] 2 (5)
where j = 1, 2. The measure of the conditional variance as given in Equation (5) is conditional on available information and is aggregated across regimes.
Cheung and Ng’s [
k ( j / M ) = { 1 − | j ( M + 1 ) | , if j M + 1 ≤ 1 0 otherwise (6)
where M is the predetermined lag order. Hong [
Q 1 = { T ∑ j = 1 T − 1 k 2 ( j / M ) ρ ^ u v 2 ( j ) − C 1 T ( k ) } { 2 D 1 T ( k ) } 1 / 2 (7)
where u ^ i , t and v ^ i , t are the standardized residuals obtained from the GARCH class of model, and
ρ ^ u v ( j ) = { C ^ u u ( 0 ) ⋅ C ^ v v ( 0 ) } − 1 / 2 C ^ u v (j)
is the sample cross-correlation between the centered standardized residuals (for testing causality-in-mean) or centered squared standardized residuals (for testing causality-in-variance) from the univariate GARCH class of models for series X and Y, and
C ^ u v ( j ) = { 1 T ∑ t = j + 1 T u ^ t v ^ t − j , j ≥ 0 1 T ∑ t = j + 1 T u ^ t + j v ^ t , j < 0
C ^ u u ( 0 ) = 1 T ∑ t = j + 1 T u ^ t 2 and C ^ v v ( 0 ) = 1 T ∑ t = j + 1 T v ^ t 2
C 1 T ( k ) = ∑ j = 1 T − 1 ( 1 − j T ) k 2 ( j / M )
and
D 1 T ( k ) = ∑ j = 1 T − 1 ( 1 − j T ) { 1 − ( j + 1 ) T } k 4 ( j / M )
The null hypothesis for the Q1 statistic is that there is no causality-in-mean (or causality-in-variance) at all lags from X to Y.
In order to examine the causal linkages in advanced European and Asian emerging markets as suggested by FTSE (Financial Times and the London Stock Exchange) Group, we use weekly price data of six indices associated with the respective economies: Czech Republic (PX index, an index of major stocks traded on the Prague Stock Exchange), Hungary (BUX, an index of blue-chip shares listed on the Budapest Stock Exchange Ltd.), Malaysia (FTSE Bursa Malaysia Index (FBMKLCI), a capitalization-weighted index of 30 largest firms listed on Malaysian Main Market), Poland (WIG (Warszawski Indeks Giełdowy), including all companies listed on the Warsaw Stock Exchange), Taiwan (China) (TAIEX, a capitalization-weighted index of all listed common shares traded on the Taiwan (China) Stock Exchange) and Turkey (XU100 index, a capitalization-weighted index of 100 leading stocks traded on Istanbul Stock Exchange). All the data have been obtained from the Bloomberg database. The period of study for all the indices is from January 1996 to April 2012 with a total of 850 observations for each index. The weekly data are associated with Wednesday. If Wednesday is a holiday, Tuesday data points are used. We have used the country name to represent the index, i.e., Czech Republic for the PX index, Hungary for the BUX index, Poland for the WIG index, Turkey for the XU100 index, Malaysia for the FBMKLCI index and Taiwan (China) for the TAIEX index.
The trading hours of the given stock exchanges are given in
The first step in analyzing the causal inter-relationship in mean and variance is to obtain the standardized residuals. Using appropriate univariate GARCH class of models for each data series, we obtain the standardized residuals for the given series. For accounting the regime changes, we also estimate the Markov Regime Switching GARCH (MRS-GARCH) model.
Stock exchange | Local time | Greenwich mean time |
---|---|---|
Czech | 08:00 AM to 04:20 PM | 06:00 AM to 02:20 PM |
Hungary | 09:00 AM to 05:00 PM | 07:00 AM to 03:00 PM |
Poland | 09:00 AM to 05:20 PM | 07:00 AM to 03:20 PM |
Turkey | 09:30 AM to 12:30 PM, 02:00 PM to 05:30 PM | 06:30 AM to 09:30 AM, 11:00 AM to 02:30 PM |
Malaysia | 08:30 AM to 12:30 PM, 02:00 PM to 05:00 PM | 00:30 AM to 04:30 AM, 06:00 AM to 09:00 AM |
Taiwan (China) | 09:00 AM to 01:30 PM | 01:00 AM to 05:30 AM |
Czech | Hungary | Poland | Turkey | Malaysia | Taiwan (China) | |
---|---|---|---|---|---|---|
Mean | 0.086 | 0.276 | 0.176 | 0.582 | 0.048 | 0.052 |
Median | 0.366 | 0.504 | 0.316 | 0.773 | 0.143 | 0.203 |
Stdev | 3.339 | 4.071 | 3.628 | 6.071 | 3.230 | 3.524 |
Min | −16.960 | −20.054 | −17.547 | −32.837 | −13.720 | −11.607 |
Max | 13.328 | 17.829 | 22.226 | 24.305 | 27.966 | 15.674 |
Quartile 1 | −1.488 | −1.653 | −1.766 | −2.584 | −1.227 | −1.902 |
Quartile 3 | 2.032 | 2.490 | 2.186 | 3.658 | 1.384 | 2.026 |
Skewness | −0.660# | −0.623# | −0.133# | −0.298# | 0.711# | −0.150# |
Kurtosis | 3.482# | 3.381# | 3.445# | 2.892# | 10.483# | 1.326# |
JB Stat | 495.022# | 463.569# | 426.447# | 311.732# | 3987.205# | 66.436# |
ARCH-LM | 86.558# | 142.108# | 58.760# | 72.608# | 75.617# | 113.948# |
Q(20) | 63.563# | 48.164# | 40.376# | 34.143* | 58.500# | 20.497 |
ADF | −9.099# | −9.421# | −8.896# | −9.201# | −8.263# | −8.261# |
KPSS | 0.136 | 0.336 | 0.118 | 0.398† | 0.166 | 0.054 |
N | 850 | 850 | 850 | 850 | 850 | 850 |
#, * and † mean significant at 1%, 5% and 10% level of significance respectively. Where Stdev represents the standard deviation of returns and ARCH-LM indicates the Lagrange multiplier test for conditional heteroskedasticity with 10 lags, JB Stat indicates the Jarque Bera statistics, Q(20) statistic is the Ljung-Box test up to 20 lags.
Czech | Hungary | Poland | Turkey | Malaysia | Taiwan (China) | |
---|---|---|---|---|---|---|
δ | 0.298# | 0.356# | 0.343# | 0.506# | 0.215# | 0.173† |
(0.093) | (0.122) | (0.107) | (0.188) | (0.075) | (0.103) | |
α0 | 1.329# | 1.066# | 0.609# | 0.759# | 0.092 | 0.451* |
(0.202) | (0.152) | (0.112) | (0.175) | (0.069) | (0.207) |
α1 | 0.229# | 0.149# | 0.170# | 0.071# | 0.139* | 0.126# |
---|---|---|---|---|---|---|
(0.031) | (0.020) | (0.020) | (0.012) | (0.060) | (0.030) | |
β1 | 0.662# | 0.793# | 0.799# | 0.906# | 0.857# | 0.840# |
(0.034) | (0.022) | (0.018) | (0.015) | (0.057) | (0.038) | |
LL | −2154.805 | −2321.329 | −2238.407 | −2656.915 | −1954.319 | −2210.929 |
SIC | 5.108 | 5.500 | 5.305 | 6.291 | 4.636 | 5.240 |
Q(20) | 39.945# | 27.280 | 26.354 | 39.775# | 29.745† | 18.550 |
Qs(20) | 13.500 | 16.550 | 11.537 | 12.339 | 10.114 | 12.557 |
ARCH-LM | 0.446 | 1.137 | 0.531 | 0.858 | 0.450 | 0.822 |
#, * and † mean significant at 1%, 5% and 10% level of significance respectively.
Czech | Hungary | Poland | Turkey | Malaysia | Taiwan (China) | |
---|---|---|---|---|---|---|
δ(1) | −1.355# | −1.480* | −0.534* | 1.096# | −3.466# | 0.443# |
(0.411) | (0.614) | (0.265) | (0.265) | (0.452) | (0.098) | |
δ(2) | 0.603# | 0.590# | 0.526# | 0.474# | 0.304# | −5.712# |
(0.097) | (0.124) | (0.124) | (0.147) | (0.060) | (0.426) | |
α 0 ( 1 ) | 4.856# | 9.334* | 2.805# | 5.436# | 0.000 | 0.378* |
(1.828) | (3.893) | (0.694) | (2.064) | (0.671) | (0.148) | |
α 0 ( 2 ) | 0.756* | 1.400# | 1.223* | 0.119 | 0.053 | 0.000 |
(0.367) | (0.536) | (0.494) | (0.133) | (0.034) | (0.814) | |
α 1 ( 1 ) | 0.103 | 0.078 | 0.020 | 0.187* | 0.000 | 0.038* |
(0.088) | (0.097) | (0.040) | (0.075) | (0.142) | (0.021) | |
α 1 ( 2 ) | 0.007 | 0.000 | 0.000 | 0.002 | 0.115# | 0.608# |
(0.052) | (0.047) | (0.062) | (0.013) | (0.020) | (0.019) | |
β 1 ( 1 ) | 0.866# | 0.922# | 0.966# | 0.776# | 0.976# | 0.817# |
(0.148) | (0.097) | (0.043) | (0.068) | (0.260) | (0.032) | |
β 1 ( 2 ) | 0.633# | 0.678# | 0.641# | 0.943# | 0.804# | 0.392# |
(0.071) | (0.066) | (0.089) | (0.020) | (0.023) | (0.019) | |
p | 0.700# | 0.651# | 0.836# | 0.000 | 0.320* | 0.941# |
(0.099) | (0.103) | (0.047) | (0.383) | (0.148) | (0.013) | |
q | 0.892# | 0.924# | 0.901# | 0.997# | 0.957# | 0.000 |
(0.029) | (0.025) | (0.031) | (0.002) | (0.011) | (0.058) | |
LL | −2114.186 | −2284.355 | −2215.347 | −2627.958 | −1937.305 | −2188.143 |
p1 | 0.736 | 0.822 | 0.625 | 0.997 | 0.941 | 0.056 |
p2 | 0.264 | 0.178 | 0.375 | 0.003 | 0.059 | 0.944 |
SIC | 5.060 | 5.461 | 5.298 | 6.270 | 4.613 | 5.234 |
Q(20) | 32.184* | 20.532 | 26.444 | 37.321* | 29.551† | 19.647 |
Qs(20) | 11.804 | 17.393 | 12.485 | 11.976 | 9.735 | 14.493 |
ARCH-LM | 0.496 | 1.105 | 0.508 | 0.626 | 0.452 | 0.719 |
#, * and † mean significant at 1%, 5% and 10% level of significance respectively.
Insignificant values of ARCH-LM, Q(20) and Qs(20) at 5% level of significance and higher values of LL (log-likelihood function) and lower values of SIC (Schwarz information criterion) for the maximum likelihood estimates of the MRS-GARCH model indicate that the MRS-GARCH model explains the dynamics in conditional volatility in a better way than the GARCH model.
In addition, we apply Garcia and Perron’s [
L R = 2 ( L 2 − L 1 )
The appropriate MRS-GARCH model captures the dynamics of the series and produces the standardized residual which we will use to analyze the causality-in-mean and causality-in-variance. Before analyzing the causality-in-mean and causality-in-variance between different markets, it is important to test the dynamics of the standardized residuals related to the given series. We make use of the McLeod-Li test and Tsay’s Test for nonlinearity to understand the dynamics of the series (standardized residuals) which we will use for analyzing the causality-in-mean and causality-in-variance between different markets. The Null hypothesis of the McLeod-Li test is that the given time series follows an ARIMA process and the null hypothesis of the Tsay’s Test for nonlinearity is that the given time series follows an AR process.
L1 | L2 | LR | p-value | |
---|---|---|---|---|
Czech | −2154.805 | −2114.186 | 81.237# | 0.000 |
Hungary | −2321.329 | −2284.355 | 73.949# | 0.000 |
Poland | −2238.407 | −2215.347 | 46.120# | 0.000 |
Turkey | −2656.915 | −2627.958 | 57.915# | 0.000 |
Malaysia | −1954.319 | −1937.305 | 34.027# | 0.000 |
Taiwan (China) | −2210.929 | −2188.143 | 45.571# | 0.000 |
McLeod-Li test | Tsay’s Test | |
---|---|---|
Czech | 0.901 | 0.123 |
Hungary | 0.164 | 0.692 |
Poland | 0.836 | 0.735 |
Turkey | 0.985 | 0.914 |
Malaysia | 1.000 | 0.267 |
Taiwan (China) | 0.997 | 0.365 |
Next, we apply Hong’s causality tests on the standardized residuals obtained from the respective MRS-GARCH models to test the causality-in-mean relationship in advanced emerging European and Asian economies.
We also examine the indirect causal relationship among advanced emerging European and Asian countries as suggested by Hsiao [
The literature also provides evidence in support of the notion that the first order and second order causal relationships among markets may vary dynamically over time and provide different inferences in stable and volatile environments (Fujii [
M = 1 | M = 2 | M = 3 | M = 4 | |
---|---|---|---|---|
Czech Republic → Hungary | 2.698# | 2.988# | 3.561# | 4.023# |
Czech Republic → Poland | 1.104 | 1.358 | 1.906† | 2.372* |
Czech Republic → Turkey | −0.587 | −0.380 | 0.154 | 0.645 |
Czech Republic → Malaysia | −0.689 | −0.783 | −0.680 | −0.476 |
Czech Republic → Taiwan (China) | −0.024 | 0.290 | 0.697 | 1.262 |
Hungary → Czech Republic | 1.171 | 0.965 | 1.345 | 1.835† |
Hungary → Poland | 0.668 | 1.002 | 1.363 | 1.593 |
Hungary → Turkey | 0.200 | 0.205 | 0.341 | 0.537 |
Hungary → Malaysia | −0.584 | −0.507 | −0.294 | −0.066 |
Hungary → Taiwan (China) | 1.604 | 2.397* | 3.156# | 3.711# |
Poland → Czech Republic | −0.031 | 0.069 | 0.103 | 0.091 |
Poland → Hungary | −0.057 | 0.685 | 1.195 | 1.474 |
Poland → Turkey | −0.704 | −0.443 | −0.170 | 0.004 |
Poland → Malaysia | −0.449 | −0.039 | 0.182 | 0.259 |
Poland → Taiwan (China) | 1.289 | 1.657† | 1.846† | 1.892† |
Turkey → Czech Republic | −0.355 | −0.353 | −0.029 | 0.365 |
Turkey → Hungary | 3.200# | 3.748# | 4.429# | 4.964# |
Turkey → Poland | 2.786# | 2.618# | 3.101# | 3.776# |
Turkey → Malaysia | −0.431 | −0.456 | −0.450 | −0.466 |
Turkey → Taiwan (China) | −0.350 | 0.591 | 1.450 | 1.975* |
Malaysia → Czech Republic | 0.693 | 0.760 | 1.190 | 1.609 |
Malaysia → Hungary | 2.627# | 2.408* | 2.547* | 2.748# |
Malaysia → Poland | 2.306* | 2.196* | 2.577* | 3.035# |
Malaysia → Turkey | −0.465 | −0.419 | −0.292 | −0.094 |
Malaysia → Taiwan (China) | 4.138# | 4.070# | 3.942# | 3.796# |
Taiwan (China) → Czech Republic | 1.301 | 1.357 | 1.700† | 2.025* |
Taiwan (China) → Hungary | 3.954# | 4.257# | 4.465# | 4.598# |
Taiwan (China) → Poland | 6.024# | 6.135# | 6.209# | 6.186# |
Taiwan (China) → Turkey | 0.215 | 0.734 | 1.118 | 1.293 |
Taiwan (China) → Malaysia | 0.692 | 0.708 | 0.628 | 0.492 |
#, * and † mean significant at 1%, 5% and 10% level of significance, respectively.
M = 1 | M = 2 | M = 3 | M = 4 | |
---|---|---|---|---|
Czech Republic → Hungary | −0.610 | −0.587 | −0.611 | −0.546 |
Czech Republic → Poland | −0.701 | −0.686 | −0.718 | −0.789 |
Czech Republic → Turkey | −0.047 | −0.208 | −0.357 | −0.487 |
Czech Republic → Malaysia | −0.706 | −0.824 | −0.700 | −0.493 |
Czech Republic → Taiwan (China) | 0.023 | −0.149 | −0.325 | −0.459 |
Hungary → Czech Republic | −0.685 | −0.710 | −0.754 | −0.793 |
Hungary → Poland | −0.704 | −0.846 | −0.972 | −1.084 |
Hungary → Turkey | −0.596 | −0.699 | −0.704 | −0.663 |
Hungary → Malaysia | 0.706 | 0.513 | 0.286 | 0.124 |
Hungary → Taiwan (China) | −0.655 | −0.269 | −0.043 | 0.006 |
Poland → Czech Republic | 0.687 | 0.507 | 0.292 | 0.099 |
Poland → Hungary | −0.556 | −0.699 | −0.805 | −0.883 |
Poland → Turkey | −0.486 | −0.636 | −0.530 | −0.384 |
Poland → Malaysia | 0.352 | 0.356 | 0.427 | 0.475 |
Poland → Taiwan (China) | −0.654 | −0.568 | −0.518 | −0.533 |
Turkey → Czech Republic | 0.213 | 0.083 | −0.079 | −0.239 |
Turkey → Hungary | 0.561 | 0.387 | 0.201 | 0.058 |
Turkey → Poland | −0.633 | −0.781 | −0.863 | −0.922 |
Turkey → Malaysia | −0.708 | −0.830 | −0.936 | −1.008 |
Turkey → Taiwan (China) | −0.253 | 0.491 | 0.926 | 1.052 |
Malaysia → Czech Republic | 1.377 | 1.277 | 1.094 | 0.933 |
Malaysia → Hungary | 7.660# | 7.298# | 6.674# | 6.073# |
Malaysia → Poland | 8.254# | 7.870# | 7.235# | 6.628# |
Malaysia → Turkey | −0.503 | −0.658 | −0.808 | −0.934 |
Malaysia → Taiwan (China) | −0.543 | −0.670 | −0.728 | −0.772 |
Taiwan (China) → Czech Republic | −0.705 | −0.832 | −0.852 | −0.823 |
Taiwan (China) → Hungary | −0.426 | −0.561 | −0.678 | −0.773 |
Taiwan (China) → Poland | −0.677 | −0.464 | −0.352 | −0.352 |
Taiwan (China) → Turkey | −0.312 | −0.346 | −0.389 | −0.441 |
Taiwan (China) → Malaysia | 0.027 | −0.064 | −0.163 | −0.267 |
#, * and † mean significant at 1%, 5% and 10% level of significance, respectively.
This paper examines the causal linkages among advanced emerging European and Asian economies using weekly data of their stock indices over the sample period January 1996 to April 2012. We apply Hong’s [
Our findings suggest that institutional investors and portfolio managers should consider causal linkages among stock markets while investing in offshore markets for diversification benefits. In particular, our findings will be of value to investors investing in multiple markets having different economic conditions who are concerned about the return and volatility spillover among markets. In addition, our findings have important implications towards implementing trading strategies and the evaluation of investment and asset allocation decisions by portfolio managers, financial analysts and institutional investors such as pension funds.
The author declares no conflicts of interest regarding the publication of this paper.
Kumar, D. (2019) Causal Linkages among Advanced Emerging European and Asian Economies. Theoretical Economics Letters, 9, 139-154. https://doi.org/10.4236/tel.2019.91012