Data description Unit roots test

Section 4 introduces the forecast error variance decomposition model and its result. Section 5 summarizes and concludes the paper.

2. Data description

The data consist of daily closing prices for the New York SP 500 index and the following 11 major Asia – Pacific equity market indices: Tokyo Nikkei 225, Hong Kong Hang-Seng, Singapore Straits Times, Sydney All Ordinaries, Seoul Com- posite Index, Taiwan Composite Index, Kuala Lumpur Composite Index, Manila Composite Index, Bangkok Composite Index, Jakarta Composite Index and Shang- hai B-shares index. The prices are collected for the period from July 1, 1996 to June 30, 1998. To investigate the possible differences of cointegrational relationship among the 12 stock market indices before and during the Asian crisis, the data are divided into two groups: 1. July 1, 1996 – June 30, 1997: the period before the crisis. 2. July 1, 1997 – June 30, 1998: the period during the crisis. All daily index prices are taken a natural logarithm ln in front. Table 1 shows statistical characteristics in the 12 country indices. We also plot the 12 indices time series in Fig. 1 for the period before the crisis and for the period during the crisis. In order to ensure the same number of observations, we omitted all the observa- tions from Saturday’s trading mainly in Bangkok, Taiwan and Seoul. For a specific not common holiday in a country, we use the preceding day’s observation as a proxy for that day.

3. Unit roots test

Following the discussion by Dickey and Fuller 1979, 1981, consider the time series of x t has the pth-order autoregressive process: x t = a + a 1 x t-1 + a 2 x t-2 + ... + a p x t − p + o t 1 The representation can be transformed and added by a time-trend term. Dx t = a + rx t − 1 + a 2 t + p i = 2 b i Dx t − r + 1 + o t 2 r = 1 − p i = 1 a i n b = p j = i a j In the above Augmented Dickey – Fuller test, the null hypothesis is H : r = 0. If this is true, x t has a unit root. Dickey and Fuller 1979 found that the critical values for r = 0 depend on the form of the regression and sample size. With 100 observations, there are three different critical values for the t-statistic r = 0. For a regression without the intercept and trend term a = a 2 = 0, use the section labeled H .- C . Sheng , A .H . Tu J . of Multi . Fin . Manag . 10 2000 345 – 365 349 Table 1 Statistical characteristics of the 12 countries’ indices Number of Standard Sample period Variance Skewness Kurtosis Minimum Maximum Average observation deviation 0.1907 SP 500 − 0.7343 Before 626.64 898.70 254 747.80 68.95 6.36 0.4177 − 1.4247 876.99 1138.49 5.84 250 During 76.52 1003.32 Before 85.40 − 0.4229 − 1.0957 17303.65 22455.49 247 19969.19 Nikkei225 1305.90 1548.46 141.44 0.7275 − 0.3895 14664.44 20575.26 246 16952.13 During 2.68 − 0.1712 − 0.9962 1974.37 2136.59 2291.53 Singapore Straits 245 Before 75.67 Times During 43.63 − 0.0408 − 0.7486 1048.96 2007.23 248 1617.68 265.68 Before 133.33 7.46 0.3362 0.0507 2096.10 2725.90 249 Sydney All 2383.02 Ordinaries − 0.3164 0.1107 2299.20 2881.40 99.76 3.74 2661.98 251 During 60.67 4.98 0.1653 − 1.0387 611.05 858.79 246 Seoul Composite 738.91 Before 0.3115 − 0.9322 280.00 781.70 37.45 518.36 267 During 139.33 886.94 Before 108.44 0.3535 − 1.3545 5955.50 9030.28 289 7254.29 Taiwan Composite 0.1788 − 0.9336 7089.56 10116.84 During 277 8584.19 762.68 67.76 105.17 − 0.0563 − 0.7379 10585.86 12713.86 15196.79 Hong Kong 1156.31 251 Before Hang-Seng During 518.05 0.5613 − 0.9126 7462.50 16673.27 246 11671.74 2458.97 3.15 0.1536 − 1.2461 1041.27 1271.57 60.41 Before 1158.53 249 Kuala Lumpur Composite 36.95 During 0.5549 − 0.4143 435.84 1084.88 246 704.77 161.38 202.14 Before 13.22 − 0.8301 0.0797 2499.00 3448.00 245 3090.23 Manila Composite 0.6193 − 0.1284 1518.00 2816.00 280.51 During 37.55 2095.45 249 H .- C . Sheng , A .H . Tu J . of Multi . Fin . Manag . 10 2000 345 – 365 350 Table 1 Continued Standard Number of Sample period Variance Skewness Kurtosis Minimum Maximum Average observation deviation 853.08 203.06 48.34 0.0523 − 0.9347 464.77 1268.20 Bangkok 246 Before Composite − 0.0160 − 0.6428 257.44 682.16 103.23 22.69 469.58 244 During Before 54.59 4.76 − 0.0988 − 1.3150 530.89 725.00 257 Jakarta Compo- 626.52 site 0.9264 0.2125 340.00 741.00 99.66 During 504.11 248 19.70 3.42 0.5438 − 0.9786 44.87 Shanghai B- 98.21 Before 244 63.90 14.79 Shares 0.4320 − 0.9584 39.44 90.36 13.15 During 2.84 60.96 244 t . Including an intercept term but not a trend term a 2 = 0 only, use the section labeled t m . Finally, with both intercept and trend, use the section labeled t t ., Table 2 lists critical values for 95 and 99 confidence intervals for t-statistic t, t m and t t . Dickey and Fuller 1981 provided three additional F-statistics f 1 , f 2 and f 3 to test joint hypothesis on the coefficients. The null hypothesis r = a = 0 is tested using the f 1 statistic. Including a time trend in the regression, the joint hypothesis a = r = a 2 = 0 is tested using the f 2 , statistic and the joint hypothesis r = a 2 = 0 is tested using the f 3 statistic. Table 3 also provides critical values for 95 and 99 confidence intervals for t-statistic f 1 , f 2 and f 3 . Fig. 1. Time series plots for 12 country indices. Fig. 1. Continued Finally, it is possible to test hypotheses concerning the significance of the drift term a and time trend a 2 . Under the null hypothesis r = 0, the test for the presence of the time trend is given by the t bt statistic. Thus, the statistic is the test a 2 = given that r = 0. Similarly, to test the hypothesis a = 0 given that r = 0 use the t at and to test the hypothesis a = 0 given that r = 0 and a 2 = 0, use the t am . The critical H .- C . Sheng , A .H . Tu J . of Multi . Fin . Manag . 10 2000 345 – 365 353 Table 2 Summary results of unit roots tests a South Korea US Taiwan Hong Kong Malaysia The Philippines Thailand Indonesia China Japan Singapore Australia Country I1 I1 I1 I1 I1 I1 I0 I1 I1 I1 I1 I1 Before the crisis I1 I1 I1 I1 I1 I1 I1 I1 During the crisis I1 I1 I1 I1 a In denotes integration of order n; I1 denotes unit root and I0 denotes stationarity. The test statistics can be provided by the corresponding author on request. values of 95 and 99 confidence intervals for t bt , t at and t am are also listed in Table 3. Unless the researcher knows the actual data-generating process, it is questionable as to whether it is appropriate to estimate. Hence, we consider the following three alternatives of Eq. 2. Dx t = rx t − 1 + p i = 2 b i Dx t − r + 1 + o t 2a Dx t = a + rx t − 1 + p i = 2 b i Dx t − r + 1 + o t 2b Dx t = a + rx t − 1 + a 2 t + p i = 2 b i Dx t − r + 1 + o t 2c It might seem reasonable to test the hypothesis r = 0 using the most general of the models of Eq. 2. For example, if the true process is a random walk, this regression should find that a0 = r = a 2 = 0. One problem with this line of reasoning is that the presence of the redundant estimated parameters reduces degrees of freedom and the power of the test. In other words, there is the possibility that the research will conclude that the process contains a unit root, where, in fact, none is present. Campbell and Perron 1991 found four important difficulties concerning the unit root tests. These difficulties imply that the research may fail to reject the null hypothesis of a unit root because of a mis-specification concerning the deterministic part of the regression. Too few or too many regressors may cause a failure of the Table 3 Summary of the Dickey–Fuller Tests Test statistic Hypothesis Critical values for 95 and 99 confidence Model intervals for sample size of 100 a t t Dx 1 = a + rx t−1 r = 0 − 3.45 and −4.04 + a 2 t+o t t at 3.11 and 3.78 a = 0 given r = 0 t bt 2.79 and 3.53 a 2 = 0 given r = 0 6.49 and 8.73 f 3 r = a 2 = a = r = a 2 = f 2 4.88 and 6.50 r = 0 Dx t = a + rx t−1 t m − 2.89 and −3.51 + o t a = 0 given 2.54 and 3.22 t am r = 0 4.71 and 6.70 f 1 a = r = 0 r = 0 Dx t = rx t−1 +o t t − 1.95 and −2.60 a Source, Enders 1995, or Dickey and Fuller 1979, 1981. test to reject the null of a unit root 2 . To avoid the inappropriate use of a unit root test, we follow the procedure suggested by Doldado et al. 1990. The empirical results of unit root tests are summarized in Table 2. Before the crisis, the calculated values of test statistics, with the exception of Thailand, are all smaller than their corresponding critical values at 5 significance level. We do not reject the null hypothesis that the 11 indices not Thailand contain a unit root. During the period of the crisis, the calculated values of test statistics of all 12 indices are smaller than their corresponding critical values at 5 significance level. We do not reject the null hypothesis that the 12 indices all contain a unit root.

4. Cointegration and causality