Unit Root Tests of Structural Break with GARCH-error Process

This paper studies the effect of GARCH process on the robustness and reliabilities of unit roots test with structural breaks. It gives that, as the GARCH process approaches integratedness, the test statistic' the proportion of rejections reported actually increases as the sample size increases. Consequently, we can see that the standard asymptotic theory is inapplicable in this case. The statistic t(alpha)*(3), their actual test size on the whole is accordant to nominal size in unit root and no break as the volatility parameter is small, phi(1)=0 or approach to 0. The statistic exists a serious over sizing of null hypothesis as integratedness in all structural break type. The statistic test power increases as the sample size increases, but test power do not increases as the sample size increase under AR parameter. Test power increases as integratedness increases, and decreases as volatility parameter increases.