Statistic Distribution and Simulation Analysis for Unit Root Test with I(2) Variable

Based on the theoretical derivation and Monte Carlo simulation, the statistics distribution of classical DF test with I(2) variable were studied, and the test effect was examined when the critical value was misused. The theoretical research shows that these test statistics converge in large samples to the function of Wiener process under the null hypothesis, which are different from the classical unit root test statistics. The simulation result indicates that, though the critical value is obviously different, the coefficient test statistic has a satisfactory effect, while the test results of the pseudo t test statistic depend on the test configuration. It is concluded that the statistic critical value of the classical unit root test can be used to test the I(2) variable, but it should be combined with the two kinds of test statistics rather than the pseudo t test statistics itself.