Impact of opening up of the Taiwan futures market to foreign investors : price effects of foreign investment liberalization: empirical analysis.
This paper investigates the impact of the opening up of the Taiwan futures market to foreign investors on the price discovery function and volatility of the local futures market. The additional market factor effects are controlled and the asymmetric response behavior is studied. Major results are as follows. First, the evidence suggests that foreign investment liberalization increases the number of informed traders and leads to improve the price discovery function of the Taiwan futures market. Second, the level of futures price volatility increases and the asymmetric responses of volatility to news have reduced following futures markets liberalization. These results imply that increased participation of informed foreign investors in emerging futures market should enhance the rate of information flow, improve the quality and reliability of information and, hence, reduce the impact of noise traders on price volatility. Our findings provide important information to policymakers considering opening up their markets to foreign investors.
Key words: Liberalization, Emerging Futures Market, Foreign Investors, Price Volatility JEL Classification: F21, F29, G15, N15
The financial liberalization process followed by emerging markets during the last twenty has attracted the attention of a number of researchers. (1 to 10) This issue regarding the impacts of foreign investors trading on the local financial market is concentrated on the stabilizing or destabilizing role of foreign investors. The supporters argue that the well-informed foreign institutional investors whose investment strategies base more on fundamentals are helpful to the market microstructure, mitigate the impact of noise trading, and tend to stabilize the financial market. In contrast, the dissenters stress that short-run volatility will be increased and the degree influenced by international markets will be enlarged because of the quicker pace and inherent uncertain characteristic of foreign investors trading. It can have a destabilizing effect on the financial markets and real economy." While empirical results show no agreements in this issue, the introduction of foreign investors into financial markets still continues all over the world.
Taiwan stock market has become an increasingly popular investment destination in the Asian stock markets, particularly since the Taiwan Stock Index (TSI) is introduced into the Morgan-Stanley Emerging Market Free Index, World Free Index and Fareast Free index. Taiwan Futures Exchange (TAIFEX) introduced the first futures contract based on Taiwan's stock market indices on July 21, 1998, which is an important milestone for the development of Taiwan financial market. Because local investors are less familiar with the properties and trading mechanism of futures products, the Taiwan futures market is not active in earlier period. In order to increase the width and depth of the Taiwan futures market, government authority allowed the opening up of Taiwan futures markets to foreign investors (QFIIs)* on November 1, 1999.
Previous studies regarding the impact of foreign institutional investors on Taiwan's stock and foreign exchange markets have been conducted, (10 to 12) but relatively little empirical work has been done to study the issue of how the opening up of the Taiwan futures market to foreign investors affects the local futures market. Consequently, this paper will bridge a gap in the literature. The empirical results may provide insights for authorities' decisions. Also, Taiwan's experience in this study may function as a guide for other developing countries, which are in a quandary over the influences of foreign institutional investors.
The purpose of this paper is to produce a marginal contribution to this literature by investigating the price effects of futures market liberalization in Taiwan. In particular, this study concentrates on two issues. First, we employ the error correction model (Engle and Granger (13)) to examine the cointegration and lead-lag relationships between the spot and futures markets in Taiwan, both before and after the opening up of futures market to foreign investors (QFIIs). Most of the empirical studies document that futures markets are more likely to incorporate information more efficiently than spot markets, and serve a more important role in price discovery. (14 to 20) On the contrary, Huang and Shyu (21) and Hsu and Ho (22) report that the price discovery process is originated primarily from the spot market in Taiwan. Supporters of foreign investment stress that, because of its demonstration effects, it has a positive effect on local financial markets in the host country. Arbel and Strebel (23) find that individual investors tend to follow institutional investors' trading activities. Consequently, we will examine whether increased openness for foreign investors (QFIIs) may lead to an increase in the number and influence of informed traders in the local futures market and, hence, improve the price discovery function of the Taiwan futures market.
Second, this study adopts a GJR-GARCH model to examine the level of volatility and the asymmetric response of volatility to news in the Taiwan futures market, both before and after the opening up of futures market to foreign investors (QFIIs). There are two contrasting arguments regarding the possible impacts of foreign investors on market volatility. One suggests that foreign investors can destabilize the market and volatility will increase because of the quicker pace of transactions. The other views foreign investors as having a positive effect on the market by increasing the information flow to the market and reducing the impact of noise traders on price volatility. Although numerous studies regarding this stabilization-destabilization issue have been undertaken, the results show no consistency. Even if volatility increases, this may not be damaging to the markets. The recent studies reported by Edward (24), Bollerslev, et al. (25), Ross (26), Blume, Easley, and O'Hara (27), Antoniou and Holmes (28), suggest that it is the volatility of an asset's price, not only the asset's simple price change, that is correlated to the rate of information flow, so increased volatility should not be simply regarded as disadvantageous in the traditional view. Hence, increasing volatility could be the result of increased information flow, which could make the market more efficient (Lamoureux and Lastrapes (29)).
In this paper, there is one distinctive feature on purpose that QFIIs impacts can be more robust. The hypothesis that market factors other than QFIIs introduction may have affected futures market volatility, so the additional market factors effects are controlled in this paper. For this purpose the Taiwan Stock Index (TSI) is included as a proxy for additional market factors in the mean equation of the GJR-GARCH model, so that impact of QFIIs trading on the futures price volatility is correctly investigated without contamination.
This article uses the daily closing prices of the Taiwan Stock Exchange Value-Weighted Stock Index and the Taiwan Stock Index Futures nearby contracts traded on TAIFEX. The data for the futures and spot prices are retrieved from the Taiwan Futures Exchange (TAIFEX) and the Taiwan Economic Journal (TEJ)** database, respectively. The spot returns RS and futures returns, RF database, respectively. The spot returns, [R.sub.s] and futures returns, RP, are obtained by taking the natural logarithmic difference of the price levels, respectively. That is, [R.sub.st] = [S.sub.t] - [R.sub.t-l] and [R.sub.Ft] = [F.sub.t] - [F.sub.t-l] where [F.sub.t] is the logarithm of the futures prices, and St is the natural logarithm of underlying spot price.
The sample period under investigation is from July 21, 1998 to February 20, 2001, which is equally split into two subperiods (pre- and post-liberalization periods). To do so allows a comparison before and after the participation of QFIIs. The cut-off point is November 1, 1999, when the local authority allowed the opening up of Taiwan futures markets to the foreign investors (QFIIs). Consequently, the pre- liberalization period is from July 21, 1998 to October 31, 1999; and the post-liberalization period is from November 1, 1999 to February 20, 2001.
Table 1 presents descriptive statistics of the spot and futures returns series for the pre- and postliberalization periods, respectively. It is noticeable that the standard deviations of the spot and futures returns in post-liberalization period are higher than in preliberalization period. This reveals that futures market volatility increases following futures liberalization. The kurtosis measures and Jarque-Bera statistics are statistically significant at the 5% level for the two subperiods, indicating that none of the return series is normally distributed. The Ljung-Box statistics, denoted by Q (6) and Q (12), for testing the null hypothesis of no dependency on return series up to 6 and 12 orders, show that the null hypothesis is not rejected at the 5% level of significance in both the futures and spot return series for the pre-liberalization period. However, the null is rejected for the post-liberalization period, indicating that the first moment autocorrelations are present. In addition, we examine the dependence on the squared returns by using Ljung-Box statistics, denoted by Q2 (6). The evidence shows that the Q2 (6) statistics are statistically significant at the 5% level for all four return series in the two subperiods, suggesting that the two return series are characterized by the second moment dependence and the variances of the futures and spot returns change over time for the two subperiods, namely ARCH effect. We further test whether the return series exist ARCH effect by utilizing LM test proposed by Engle (30) and the result also shows that ARCH (6) statistics are statistically significant for all four return series in the two subperiods. Consequently, this paper will employ GARCH-type process (Engle; Bollerslev, (31); Bollerslev et al., (25)) to model futures price volatility.
Cointegration and price discovery
Engle and Granger show that two 1(1) series, S, and [F.sub.t], are said to be cointegrated if there exists a linear combination of the two series for the constant, [alpha], such that [Z.sub.t] = pS.sub.t] -[alpha][F.sub.t] is a stationary process, i.e., 1(0). a is the cointegrating parameter and Z, is the equilibrium error. Cointegration implies there exists a long-run equilibrium relationship between there two series. This article utilizes the cointegration test proposed by Johansen and Juselius (32) to investigate whether the cointegration between the spot and futures markets in Taiwan exists for the pre- and post-liberalization periods.
The Granger Representation Theorem provided by Engle and Granger indicates that the cointegration system can be equivalently represented by a unique error correction model (ECM). For cointegrated series, tests of Granger causality need to be performed in the corresponding ECM framework and can be used to examine the short-run dynamics with a long-run equilibrium relationship. Therefore, this paper will employ the following ECM framework to investigate whether futures or spot markets performs most of the price discovery function for the pre- and post-liberalization periods.
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
where [DELTA][F.sub.t] and [DELTA][S.sub.t] denote the first differences in the natural logarithm of the futures price and spot prices, respectively; and ([S.sub.t-l] - [alpha][F.sub.t-1]) is the previous period's equilibrium error, namely the error correction term, which expresses the deviations from a "long-run" cointegration equilibrium in the last period. The appropriate lag-length specification-of each equation is determined by using Akaike's Inforniation Criterion(AIC). The coefficient [[beta].sub.F] and [[beta].sub.s] represent the adjustment speeds of error correction mechanism in [DELTA][F.sub.t] and [DELTA][S.sub.t], respectively, toward long-run equilibrium cointegration relation. If the coefficient of, [s.sub.t-l], error correction term in the process of [F.sub.t]([S.sub.t]), is small, [F.sub.t] ([S.sub.t]) has little tendency to adjust a disequilibrium situation. That is, most of the adjustment will be done by [S.sub.t] ([F.sub.t]), and futures (spot) plays a more important role in price discovery. Besides, the Granger-causality tests between futures and spot are investigated by testing whether all the coefficients [b.sub.i] or [c.sub.i] are jointly different from zero, based on a standard F-test. If some b are statistically different from zero but some [c.sub.i] not, then we says spot Granger-causes futures. Similarly, futures Granger-causes spot if some c, are statistically different from zero but some [b.sub.i] not. This indicates that there is a unidirectional causality between futures and spot markets. Moreover, if both [b.sub.i] and [c.sub.i] are significantly different from zero, there is a feedback relationship between futures and spot markets.
Impact of QFIIs Trading on Futures Market Volatility Considering Market Factors
The fact that the variance of asset returns changes over time is well documented in financial literature. This type of behavior has been modeled very successfully with ARCH or GARCH model*. In particular, the GARCH(1,1) (25,31,33,34) has been extensively showed to be the most parsimonious representation of conditional variance that best captures volatility clustering in many financial time series. But this model is connected with the shortcoming that it assumes a symmetric response to news and fails to account for observed asymmetry in the market. In order to examine the impact of the opening up of the futures market to QFIIs on the level and nature of futures price volatility, this study employs the GJR-GARCH(1,1) model which is proposed by Glosten et al. (35) and allows for asymmetric responses to information.
To investigate correctly the impact of QFIIs trading introduction on the futures price volatility without contamination, the behaviour of the futures index return is adjusted for exposition to other market factors which may affect futures market volatility. Following Bologna and Cavallo (36), this study the spot return** is used as a proxy for market factors. The adjustment is obtained by including spot return as exogenous explanatory variables in the mean equation of the GJR-GARCH model. The GJR-GARCH(1,1) model is specified as follows and is estimated for the pre- and post-liberalization periods, respectively.
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)
[h.sub.t] = =[[omega].sub.0] + [[omega].sub.1] [[epsilon].sup.2.sub.t-1] + [[omega].sub.2] [h.sub.t-1] + [[omega].sub.3] [[epsilon].sub.3] [[epsilon].sup.2.sub.t-1] [D.sub.t-1] (4)
where Equation 3 is the conditional mean equation; [R.sub.F,t] and [R.sub.S,t] denote the futures and spot returns at time t. [R.sub.F,t] is regressed on its AR(p) process so as to eliminate the serially correlated residuals in Equation 3. [[OMEGA].sub.t-1] is the information set available up to time t. Equation 4 is the conditional variance equation and h, represents the conditional variance term at time t. We can examine the level of volatility through the [[omega].sub.0] coefficient. The value of increases in the post-liberalization period, implying that liberalization has led to a increase in the level of futures market volatility. [D.sub.t-1] is a dummy variable which is 1 in response to bad news ([[epsilon].sub.t-1]) and zero in response to good news ([[epsilon].sub.t-1]>0). If [[omega].sub.0] is positive, an asymmetric effect exists in the data as a negative return will increase the volatility more than does a positive return of the same magnitude. Therefore, coefficient [[omega].sub.0] measures the extent to which there is an asymmetric response of volatility to news and its changes from pre-liberalization to postliberalization is important in our analysis. A decrease in the value of [[omega].sub.0] in the post-liberalization period will imply that the impact of noise traders has decreased as a result of the opening up of futures market to QFIIs, whereas a rise in [[omega].sub.0] will suggest the opposite.
In addition, different from the above partitioning of the whole period, an alternative modeling of volatility, namely a switching GJR-GARCH(1,1) model, is employed to increase the robustness of this study. Lee and Ohk (37) present the modified GARCH, which imposes an autoregressive structure on conditional variance and captures the change in the level and slope of time-varying volatility using dummy variables. This modified model is called the switching GARCH model. Hence, in the spirit of Lee and Ohk, Equation 4 is reestimated for the whole period with a dummy variable included to investigate the impact of the opening up of the futures market to QFIIs on the level and asymmetry of futures price volatility. The dummy variable, namely switching point t* (November 1, 1999), takes on the value 0 in the preliberalization period and 1 in the post-liberalization period. Consequently, the modified model, switching GJR-GARCH(1,1), can be specified as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)
where is a dummy variable that is 1 if t [??] t* and [D.sub.t-1] is 0 otherwise, and is 1 if [[epsilon].sub.t-1] and 0 otherwise. Consequently, we can investigate whether futures price volatility structure change after opening up the futures market to QFIIs by examining the coefficients on the dummy variables. The Berndt-Hall-Hall-Hausman (38) optimization algorithm is used to calculate maximum likelihood estimates of each of the coefficients in the conditional mean and variance equations.
Cointegration and Price Discovery
Before cointegrtion test is performed, it is necessary to ensure that the price series are integrated of the same order. The order of integration of a nonstationary time series can be inferred by testing for unit root. This paper uses the augmented Dickey-Fuller (ADF) (39) test to detect whether unit roots exist in both spot and futures price series for the pre- and post-liberalization periods. Panel A of Table 2 shows that the unit root hypothesis in each original price series cannot be rejected at the 1% and 5% significance level. Nevertheless, all four price series are transformed to achieve stationarity by taking the first difference of the natural logarithm of each orignal price series. This results suggest that the spot and futures index prices are nonstationary I(1) series, which fulfills the necessary condition for cointegration test.
The results of the cointegration test are presented in Panel B of Table 2. Obviously, the Taiwan stock index futures and spot are cointegrated at the 5% significance level for the pre- and post-liberalization periods, suggesting that there exists a long-run equilibrium relationship between these two price series. However, there is an interesting finding that the cointegration relation is still statistically significant at the 1% level during the post-liberalization period but not during the preliberalization period. Therefore, this evidence shows that the openness to QFIIs may make the cointegration between the index spot and futures series more stable.
After confirming that these two price series are 1(1) and cointegrated for both periods, the ECM is used to examine whether the information transmissions process (lead-lag patterns) between the index spot and futures are different for the pre- and post-liberalization periods. Table 3 reports the estimates of the error correction model. For the pre-liberalization period, based on the F-statistics, the null hypothesis of all [b.sub.i] = 0 is rejected at the 5% significance level, but the null hypothesis of all [c.sub.i] = 0 is not rejected. This shows that the information flow is from the index spot market to the index futures market, implying that spot Granger-causes futures in the pre-liberalization +period. Additionally, the error correction coefficient [[beta].sub.F] is statistically significant in the futures index equation, [DELTA][F.sub.t] (t-statistic: 2.86), but [[beta].sub.S] is not significant in the spot index equation, [DELTA][S.sub.t] (t-statistic: 0.65), indicating that most of the adjustment is made through the futures market when disequilibrium occurs in the pre-liberalization period. However, after the opening up of the local futures market to QFIIs, the results are opposite. For the postliberalization period, the null hypothesis of all causal coefficients [c.sub.i] and the error correction coefficient [[beta].sub.s] are statistically rejected at the 5% significance level, but the joint test of all causal coefficients [b.sub.i] and the t-statistic of the error correction coefficient [[beta].sub.F] are not statistically significant. This results illustrate that futures predominantly Granger-causes spot in the post-liberalization period and most of the adjustment is made through the spot market when disequilibrium occurs.
In general, the price discovery function of futures markets has long been documented in the theoretical and empirical literature. (15 to 20,38,40,41) The conclusions from Table 3 show remarkably that the opening up of the local futures market to QFIIs has indeed improved the price discovery function of the Taiwan futures market.
Impact of QFIIs trading on futures market volatility considering market factors
Table 4 shows the parameter estimates of GJR-GARCH(1,1) models of the Equations 3 and 4 for both periods, allowing a comparison of the level and nature of volatility before and after the opening up the Taiwan futures market to QFIIs. In the conditional mean equation, it is striking to note that the coefficient of [R.sub.S,t-1] is statistically significant at the 5% level in the preliberalization period, suggesting that spot leads futures. However, the coefficient of [R.sub.S,t-1] is not statistically significant in the post-liberalization period, implying that a lead from spot-to-futures is no more detected. This finding is consistent with the above evidence based on ECM.
In the asymmetric conditional volatility equation, the parameters are statistically significant at the 5% level for both pre- and post-liberalization periods, with the exception of the constant term in the pre-liberalization period. First, we can examine the level of volatility through the [[omega].sub.0] coefficient. After the opening up of the market to QFIIs, the coefficient [[omega].sub.0] increase from 0.0014% to 0.0019%, suggesting that liberalization is able to increase the speed of informational transmission to the local futures market. In order to investigate the impact of the opening up of the markets on the nature of volatility to news, we compare parameters [[omega].sub.1], [[omega].sub.2], [[omega].sub.3]) for both periods. The coefficient co which measure the impact of good news on volatility decreases from 0.074 to 0.0354, and the coefficient [[omega].sub.1] + [[omega].sub.3] for the impact of bad news also decreases from 0.2163 to 0.1345. Additionally, the coefficient co 3 for the asymmetric effect is statistically significant for both pre- and post-liberalization periods, indicating that asymmetries exist in the Taiwan futures Market. However, the results for the post-liberalization period demonstrate that the asymmetry coefficient [[omega].sub.3] have gone down from 0.1423 to 0.099, suggesting that the opening up of the futures market to QFIIs has reduced the asymmetric response of volatility to news.
In order to examine whether the models are correctly specified, Table 4 also presents the diagnostic test applied on standardized and squared standardized residuals by means of the Ljung-Box statistic and LM test. The calculated statistics show that no residual exists linear and nonlinear independence, suggesting that the GJR-GARCH(1,1) models are appropriately specified.
The estimated results of the switching GJR-GARCH(1,1) model are reported in Table 5. When we examine the sigh of the coefficients for the dummy variables, the findings confirm the previous results presented in Table 4. The [[gamma].sub.0] coefficient, indicating the change in the level of volatility, is positive, implying that the mean level of volatility increases after the opening up of the local futures markets to QFIIs. The [[gamma].sub.1] and [[gamma].sub.3] coefficients, indicating that the changes in the impact of good news and the asymmetric effect, respectively, are negative, revealing that the impact and asymmetry of volatility to news also decrease after the onset of QFIIs trading.
To sum up, these findings conclude that the opening up of the Taiwan Futures Market to informed QFIIs leads to increase the speed and quantity of information flowing into the local futures market and further improve the asymmetries caused by the noise traders*, i.e. uninformed traders.
This paper investigates the price effects of futures market liberalization in Taiwan. We examines the impact of the opening up of the Taiwan futures market to well-informed foreign investors (QFIIs) on the price discovery function and volatility of the local futures market when other market factors are controlled.
First, the result of cointegration analysis shows that the Taiwan stock index futures and spot are cointegrated for both pre- and post-liberalization periods, but the openness for QFIIs may make the cointegration relation more stable. Then, the information transmission process is examined by means of the error correction model. As a result, we find that for the pre-liberalization period, the spot price leads the futures price; whereas, for the post-liberalization period, the futures price leads the spot price. Therefore, the evidence suggests that the number of informed traders increases and this may lead to indeed improve the price discovery function of the Taiwan futures market following futures market liberalization.
With regard to futures market volatility, the level of futures price volatility increases in the post-liberalization period, suggesting that more information is transmitted to the local futures market and enhance information flows. In addition, the asymmetric effect is statistically significant for both pre- and post-liberalization periods in Taiwan futures market. However, the asymmetric response of volatility to news has fallen after the opening up of the local futures market to QFIIs. Consequently, the results support that the introduction of informed QFIIs reduces the asymmetries induced by noise traders. This finding is consistent with Holmes and Wong (10).
Overall, the above empirical evidence indicates that the introduction of well-informed QFIIs has a positive impact on the local futures market to improve market efficiency. Our results are consistent with those theories stating that well-informed foreign capital enhance the rate of information flow, improve the quality and reliability of information and, hence, reduce the impact of noise traders on price volatility, suggesting that liberalization and deregulation is appropriate.
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MINHSIEN CHIANG, Ph.D.
Institute of International Business
National Cheng Kung University
WEN-HSIU KUO, ESQ.
Department of Finance, Ling Tung College
The authors own full responsibility for the contents of the paper.
* Foreign investors in this paper refer to the qualified foreign institute investors (QFIIs). QFIIs denotes foreign investment companies which have sound financial resources and are always regarded as informed traders.
** TEJ is a private data-source company. It provides the most comprehensive and reliable economic and financial data base.
* The standard GARCH (p,q) model suggests that the conditional variance of returns is a linear function of lagged conditional variance term and past squared error terms.
** The spot return is the return of the Taiwan Stock Exchange Value-Weighted Stock Index
* Black (42), Christie (43), French, Sewert, and Stambaugh (44), Nelson (33), Engle and Ng (45), and Chiang and Wang (34) find that in both stock and futures markets, there exists an asymmetric response to news, whereby a negative shock to returns will increase volatility more than a positive shock of equal magnitude. Black argues that the asymmetric effect is much more obvious if there are many noise traders in financial markets.
TABLE 1 DESCRIPTIVE STATISTICS OF DAILY RETURNS ON THE TAIWAN STOCK INDEX FUTURES AND INDEX SPOT Pre-Liberalization (1998/7/21-1999/10/31) [R.sub.F] [R.sub.S] Mean -0.0000481 -0.0000347 Std. Dev. 0.017498 0.016389 Skewness 0.010801 0.055991 Kurtosis 5.372673 * 4.407572 * Jarque-Bera 80.69732 * 28.57778 * Ljung-Box Q (6) 1.12(0.98) 2.52(0.86) Ljung-Box Q (12) 7.40(0.83) 7.06(0.85) Ljung-Box [Q.sup.2] (6) 15.42(0.02) * 20.65(0.00) * Ljung-Box [Q.sup.2] (12) 19.11(0.08) 24.23(0.02) * ARCH (6) 5.827(0.017) * 16.19(0.012) * Post-Liberalization (1999/11/1-2001/2/20) [R.sub.F] [R.sub.S] Mean -0.00066 -0.000666 Std. Dev. 0.02255 0.019602 Skewness 0.058625 0.106563 Kurtosis 4.122275 * 3.546113 * Jarque-Bera 41.4336 * 11.18336 * Ljung-Box Q (6) 15.12(0.02) * 12.69(0.04) * Ljung-Box Q (12) 23.97(0.02) * 15.37(0.22) * Ljung-Box [Q.sup.2] (6) 103.8(0.00) * 64.94(0.00) * Ljung-Box [Q.sup.2] (12) 132.5(0.00) * 90.94(0.00) * ARCH (6) 62.13(0.00) * 43.01(0.00) * 1. The Jarque-Bera statistic tests whether a series is normally distributed under the null hypothesis of normality. 2. Ljung-Box Q (k) statistic tests the joint significance of the autocorrelations of the daily return series up to the k-th order. 3. Ljung-Box [Q.sup.2] (k) statistic tests the joint significance of the autocorrelations of the squared daily return series up to the k-th order. 4. ARCH (k) is the statistic of LM test proposed by Engle (30) and tests whether a series exists ARCH effect under the null hypothesis of no ARCH effect up to the k-th order. P-value is in parentheses. 5. * Indicate statistically significant at 5% level. TABLE 2 UNIT ROOT TEST AND COINTEGRATION TEST ON TAIWAN STOCK INDEX AND STOCK INDEX FUTURES PRICE SERIES FOR THE PRE-AND POST-LIBERALIZATION PERIODS Pre-Liberalization Post-Liberalization (1998/7/21~ (1999/11/1~ 1999/10/31) 2001/2/20) Panel A: Unit Root Test ADF Test ADF Test Index futures (In -2.8643(0.1756) -1.9585(0.6224) [F.sub.t]) Index spot (In [S.sub.t]) -2.6785(0.2463) -1.9682(0.6172) Index futures -18.2173(0.0000) ** -14.4242(0.0000) ** ([R.sub.F.t]) Index spot ([R.sub.S,t]) -17.0454(0.0000) ** -13.2581(0.0000) ** Panel B: Cointegration [[lambda].sub.Trace] [[lambda].sub.Trace] Test Critical values Critical values (5% significance (1% significance level) level) [H.sub.0] : r = 0 18.7584 * 15.41 132.4043 ** 20.04 [H.sub.0] : r [less 3.5475 3.76 1.2338 6.65 than or equal to] 0 error correction term [Z.sub.t] = [Z.sub.t] = [S.sub.t]-1.0148 [S.sub.t]-0.9843 [F.sub.t] [F.sub.t] 1. The critical values for ADF test at the 5% and 1% levels are -3.42 and -3.97, respectively. See Mackinnon (1996). [H.sub.0]: unit root, [H.sub.A] : no unit root 2. [R.sub.i,t]=ln([P.sub.i,t])-1n([P.sub.i,t-1]), i=F, S 3. r denotes the cointegrating vectors number in Panel B. 4. The number in parentheses are the p-values 5. * and ** indicate that the statistic is significant at the 5% and 1% levels, respectively. TABLE 3 ESTIMATION RESULTS OF VECTOR ERROR CORRECTION MODEL FOR TAIWAN STOCK INDEX AND STOCK INDEX FUTURES PRICE SERIES FOR THE PRE-AND POST- LIBERALIZATION PERIODS [DELTA][F.sub.t] = [[beta].sub.1] + [[beta].sub.F] ([S.sub.t-1] - [alpha][F.sub.t-1]) + [p.summation over (i=1)] [a.sub.i][DELTA][F.sub.t-i]) [p.summation over (i=1)][b.sub.i][DELTA][S.sub.t-1] + [[epsilon].sub.F.t] [DELTA][S.sub.t] = [[beta].sub.2] + [[beta].sub.S] ([S.sub.t-1] - [alpha][F.sub.t-1]) + [p.summation over (i=1)] [c.sub.i][DELTA][F.sub.t-i]) [p.summation over (i=1)][d.sub.i][DELTA][S.sub.t-1] + [[epsilon].sub.S.t] Coefficient Pre-liberalization (1998/7/21-1999/10/31) [DELTA] [DELTA] [F.sub.t] t-Stats [S.sub.t] t-Stats [[beta].sub.1] 0.00007 0.088 [[beta].sub.F] 0.2536 2.86 ** [a.sub.1] -0.3974 -3.44 ** [a.sub.2] -0.1789 -1.76 [a.sub.3] 01357 2.53 ** [b.sub.1] 0.5101 4.25 ** [a.sub.2] 0.2048 1.83 [a.sub.3] -0.0481 -1.14 [[beta].sub.2] 0.0000 -0.01 [[beta].sub.S] 0.0583 0.65 [c.sub.1] 0.0363 0.31 [c.sub.2] -0.0096 -0.09 [c.sub.3] [d.sub.1] 0.04 0.33 [d.sub.2] -0.007 -0.06 [d.sub.3] Granger Causality Test: [H.sub.0]![Gb.sub.1]= [H.sub.0]![Gb.sub.1]= [b.sub.2]=0 [b.sub.2]=0 F-Stats=9.4679 F-Stats=0.06736 (0.0000) ** (0.9349) Coefficient Post-liberalization (1999/11/1-2001/2/20) [DELTA] [DELTA] [F.sub.t] t-Stats [S.sub.t] t-Stats [[beta].sub.1] -0.0005 -0.65 [[beta].sub.F] 0.1085 1.55 [a.sub.1] 0.01561 0.21 [a.sub.2] 0.1411 2.17 ** [a.sub.3] [b.sub.1] -0.0204 -0.32 [a.sub.2] -0.0565 -1.22 [a.sub.3] [[beta].sub.2] -0.00057 -1.18 [[beta].sub.S] -0.5209 -12.28 * [c.sub.1] -0.1823 -4.12 * [c.sub.2] 0.2015. 5.12 * [c.sub.3] 0.1068 3.29 * [d.sub.1] -0.0528 -1.35 [d.sub.2] -0.0523 -1.87 [d.sub.3] 0.0276 1.078 Granger Causality Test: [H.sub.0]![Gb.sub.1]= [H.sub.0]![Gb.sub.1]= [b.sub.2]=[b.sub.3]=0 [c.sub.2]=[c.sub.3]=0 F-Stals=0.86569 F-Stats=55.3256 (0.4585) (O.0000)) ** Notes : 1. The appropriate lag-length specification of each equation is determined using Akaike's Information Criterion(AIC). The lag- length is 2 in the pre-QFIIs period and 3 in the post-QFIls period. 2. The number in parentheses are the p-values 3. * indicate that the statistic is significant at the 5% levels. TABLE 4 MAXIMUM LIKELIHOOD ESTIMATION RESULTS OF GJR-GARCH (1,1) MODEL FOR TAIWAN FUTURES MARKET FOR THE PRE-AND POST-LIBERALIZATION PERIODS [R.sub.F.t] = [[theta].sub.0] + [p.summation over (i=1)][[theta].sub.F,i][R.sub.F,t-i] + [m.summation over (j=0)][[theta].sub.S,j][R.sub.S,t-j] + [[epsilon].sub.t] [[epsilon].sub.t]|[[OMEGA].sub.t-1] ~ N(0, [h.sub.t]) [h.sub.t] = [[omega].sub.0] + [[omega].sub.1][[epsilon].sup.2.sub.t-1] + [[omega].sub.2][h.sub.t-1] + [[omega].sub.3][[epsilon].sup.2.sub.t-1][D.sub.t-1] Pre-Liberalization Post-Liberalization (1998/7/21~1999/10/31) (1999/11/1~2002/11/30) Coefficient p-value Coefficient p-value [[theta].sub.0] -0.000310 0.7145 -0.000822 0.2772 [[theta].sub.F1] -0.329738 0.0001 ** -0.071177 0.0734 [[theta].sub.S0] 0.895232 0.0000 ** 0.35246 0.0025 * [[theta].sub.S1] 0.509497 0.0000 ** 0.07090 0.0760 [[omega].sub.0] 0.000014 0.0631 0.000019 0.0036 * [[omega].sub.1] 0.074021 0.0253 ** 0.035456 0.0473 * [[omega].sub.2] 0.768271 0.0000 ** 0.761198 0.0000 * [[omega].sub.3] 0.142288 0.0092 ** 0.099092 0.0013 * [[omega].sub.1] + 0.216309 0.134548 [[omega].sub.3] Models Diagnostics Test on the Standardized Residuals Stats p-value Stats p-value LB Q(6) 3.4847 0.746 4.9610 0.549 LB [Q.sup.2](6) 1.6417 0.95 6.6779 0.352 ARCH(6) 1.565 0.955 6.1969 0.402 Notes : 1. LB Q(6) 'BLB [Q.sup.2](6) are the Ljung-Box statistics applied on the standardized and squared standardized residuals, respectively. 2. ARCH(6) is the statistics used to test whether standardized residuals exists ARCH effect up to the order. 6. 3. * indicate that the statistic is significant at the 5% levels. TABLE 5 MAXIMUM LIKELIHOOD ESTIMATION RESULTS OF THE SWITCHING GJR-GARCH (1,1) MODEL FOR TAIWAN FUTURES MARKET [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [[theta].sub.0] [[theta].sub.F,1] [[theta].sub.s,0] Coefficient -0.00 -0.08 1.02 t-statistic -0.92 -2.4 * 2.8 * [[theta].sub.s,1] [[omega].sub.0] [[omega].sub.1] Coefficient 0.73 0.00 0.09 t-statistic 1.86 1.94 2.6 * [[omega].sub.2] [[omega].sub.3] [[gamma].sub.0] Coefficient 0.75 0.18 0.001 t-statistic 10 * 2.6 * 1.12 [[gamma].sub.1] [[gamma].sub.2] [[gamma].sub.3] Coefficient -0.06 0.14 -0.09 t-statistic -1.53 1.78 -1.21 Note : * indicate that the statistic is significant at the 5% levels.
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|Author:||Chiang, Minhsien; Kuo, Wen-Hsiu|
|Publication:||Journal of Financial Management & Analysis|
|Date:||Jan 1, 2015|
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