The existing statistics in unit root tests of ESTAR-GARCH model often need to calculate the variance of specimen. In this paper, the empirical likelihood ratio statistics are proposed to deduce the limiting distribution of them, so that the random errors caused by variance calculation are avoided. And then, a critical value of the statistics can be received through simulation, the power of the QML test and the empirical likelihood ratio statistics has been compared and
studied. Monte Carlo simulation shows that compared with the QML test, the power and the criterion of tests is more fruitful and more scientific, through the empirical likelihood ratio statistics. Avoiding the random errors of the calculation of variance, the accuracy of tests is clearly increased by using the empirical likelihood ratio statistics. Finally, the empirical study of SSE can further illustrate the higher test efficiency of this statistic.