*5.2. GARCH(1,1)-X Method*

The estimated results reported in Tables 5 and 6 omit the terms of Δ*η*\_(*<sup>t</sup>* − 1) and Δ*z*\_(*<sup>t</sup>* − 1), implyingthe ignorance of EPU innovations on conditional variance. The system Equations (7) and (8) address this issue, and the estimated results using GED-GARCH(1,1)-M are reported in Tables 7 and 8. Several important findings are now summarized. First, in examining the coefficient of AR(1), autocorrelations are not significant in the G7 markets. However, autocorrelations for four markets in the Pacific-Asian group, including Australia, China, South Korea and Singapore, are significant. Viewed from this perspective, the G7 markets appear to behave more consistently with market efficiency than other markets do.

Second, the coefficients for the news variables at the current period, *ηt* and *zt*, are all negative and statistically significant; the exception is the U.S. market where the coefficient of global news is insignificant. This evidence, which shows current news variables are significant, does not go against market efficiency. However, in checking the lagged news, either one of *η<sup>t</sup>*−1, *η<sup>t</sup>*−2, *zt*−1, *zt*−2 or combinations of these lagged variables, we find the null should be rejected, indicating a lack of market efficiency. However, the patterns among the G7 markets (except for CA in the *η<sup>t</sup>*−1; JP and US in *zt*−<sup>1</sup>) appear to be more consistent as lagged one-period news are all positive and significant. This pattern reflects a market phenomenon, which shows that although the news has a negative effect on stock returns in the current period, the markets do rebound in the subsequent two periods. This pattern is also shown in the PALA markets, although the effect is not as uniform as it is in the G7 markets. Thus, the evidence in general supports the uncertainty premium hypothesis.

Third, the coefficients in the variance equation indicate that the GARCH(1,1) model in general is appropriate although some variations are found across different markets. Interestingly, testing results indicate that both Δ*η<sup>t</sup>*−<sup>1</sup> and Δ*zt*−<sup>1</sup> firmly contribute to explain variations in the variance, as evidenced by positive and significant coefficients for each market. The only exception is the Chinese market where no evidence exists to support the proposition that the variance in Chinese market volatility can be significantly predicated by EPU innovation or by its historical pattern. We further test the joint significance of all the lagged news variables in the system by setting the null as *η<sup>t</sup>*−<sup>1</sup> = *η<sup>t</sup>*−<sup>2</sup> = *zt*−1 = *zt*−2 = 0. The joint tests from the *χ*(4) indicate that the null is strongly rejected. Likewise, the joint test for Δ*η<sup>t</sup>*−<sup>1</sup> = Δ*zt*−<sup>1</sup> = 0 in the conditional variance by *χ*(2) also indicates the rejection of the null (except in the case in China); this evidence goes against the studies by Li (2017); Lopez de Carvalho (2017) and Chen et al. (2017), who fail to include the lagged EPU innovations in their models for predicting the conditional variance. The testing results thus conclude that the null hypothesis that stock returns are independent of lagged EPU innovations is rejected.



Notes: The dependent variable is stock return. The values in the first row are the estimated coefficients and in the second row are the *t*-statistics. The *ηt* is the domestic EPU at time *t*, and *zt* is the global EPU at time *t*. *χ*(4) is the chi-squared distribution for testing joint significance of lagged news in the mean equation. That is, *ηt*−1= *ηt*−2 = *zt*−1 = *zt*−2 = 0. *χ*(2) is the chi-squared distribution for testing joint significance of Δ*ηt*−1 = Δ*zt*−1 = 0 in the variance equation.

**Table 8.** Regression estimates of stock returns on domestic EPU and global EPU with GED-GARCH(1,1)-M procedure: Asian-Pacific and Latin American markets: January 1997–June 2016.


Notes: The dependent variable is stock return. The values in the first row are the estimated coefficients and in the second row are the *t*-statistics. The *ηt* is the domestic EPU at time *t*, and *zt* is the global EPU at time *t*. *χ*(4) is the chi-squared distribution for testing joint significance of lagged news in the mean equation. That is, *ηt*−1 = *ηt*−2 = *zt*−1 = *zt*−2 = 0. *χ*(2) is the chi-squared distribution for testing joint significance of Δ*ηt*−1 = Δ*zt*−1 = 0 in the variance equation.
