As it is clear that heteroscedasticity invalidates test results, it would be necessary to test formally whether heteroscedasticity is present. There are a number of famous tests for heterroscedasticity, such as Lagrange Multiplier Tests, White’s Test and Goldfeld-Quandt Test. According to the various generality and the powers of these tests, this paper applies Goldfeld-Quandt test proposed by Goldfeld and Quandt (1965), which is based on the notion that if the error variances are equal across observations, then the variance for one part of the sample will be the same as the variance for another part of the sample.
6 Here, the null hypothesis is there is no heteroscedasticity existing in the simple regression applied, mathematically H0: ? 1i?? /? 2i?? = 1, while the alternative hypothesis is the converse situation. The steps for Goldfeld-Quandt test adopted in this paper are as follows: Step1 Arrange the data set in estimated period, namely from 1 July, 2001 to 31 December 2002, including stock returns and market returns according to increasing values of market returns. 7
Step2 Divide the total ascending observation into three groups in which 143 observations for the lowest group, 98(almost 1/4 of total observation, here 370) for the intermediate group and 143 for the highest group. Step3 Omit the middle group and estimate separate regression for the remained groups respectively. Step4 Use the function in Excel to obtain the F value with 1. 158 and the critical F value in one tail with 1. 319 (See Table1). Therefore, it is concluded that the null hypothesis is accepted. In other words, there is no heteroscedasticity.
The presence of 1st-order autocorrelation is always concerned in time series data analysis. If serial correlation is present, then, that is, the error for the period t is correlated with the error for the period. The assumption of 1st-order autocorrelation is formally stated as follows: Yt= + Xt+ ut, ut =? ut-1 +? t, -1;? ;1. If it exists a perfect linear relationship between some of the Xs, then it is not possible to estimate the whole regression equation. 9 However, the regression applied in this paper is a simple regression, in other words, there is only one X. Therefore, there is no worry about the multicollinearity.
Test of Dummy Variable It is necessary to suspect some factors might produce changes in parameters of estimated equation. Change can be estimated and tested for significance. 10 This paper considers three dummy variables: Dividend, Additional Listing and Trading Statement. Run regression upon the equation as follows Rt= ? + i?? 1Rmt+i?? 2D +i?? 3 A+i?? 4T +ut, where D, A and T represents Dividend, Additional Listing and Trading Statement respectively. A variable 1 occupies the place on the day given related announcement released on that day; otherwise, variable zero takes that position.
The result of the regression shows in Table 2. From the values of the t-statistic, it is concluded that all of these dummy variable have not enough power to pressure any change of the parameters obtained from original market model. Accordingly, this model could be relied even there are similar events happening in event window in test period. In order to estimate the stock return in event window based on the market model, the stability of the regression should be guaranteed. Namely, the regression used for estimation should be consistent in its structure across time series.
Here, the Chow Test for structural change is employed which is simply an F- test can be used to determine whether a regression function differs across two different time periods. To test H0, run regression on the two successive data set and the pooled data, giving sum of squared residuals, and respectively. Secondly, test the F ratio defined by where, SSR is the sum of squared residuals from the pooled estimation, while SSR1 and SSR2 are the sum of the SSRs for the two separately estimated time periods. Thirdly, look into the F distribution form and find out the 2.
66 belong to the area which demonstrates accept null hypothesis. Consequently, the single equation can be adopted as the estimation model. Estimate the Abnormal Return Based on series of tests, the market model: Y=0. 0008+0. 7518X can be adopted in estimating the abnormal return in test period. The t-statistic of i?? is 13. 6 which indicate that the coefficient i?? is significantly substantial. The abnormal returns are obtained as the difference between observed returns of Morrison on day t and the expected returns generated by a particular benchmark model: ARt = Rt – E(Rt).
12 This paper employs a t-statistic to test the significance of the abnormal return in accordance with the method proposed by Richard S. Ruback (1983). The benchmark to test whether the t-statistic shows a significant level is 1. 96. The value of 1. 96 comes from the standard normal distribution with a mean of 0 and a standard deviation of 1. 95% of the distribution is between i?? 1. 96. If the absolute value of test is greater than 1. 96, then the abnormal return is significantly different from zero at the 5% level.