On The Asymptotics Of Bootstrap Test For Ar(p) Unit Roots

Unit root test is a very important method in testing he stationeriness of time series. Many scholares have innovated the method after Dickey and Fuller put forward ADF test in 1979. There the most effective unit root test for AR is sieve bootstrap method.Yoosoon Chang and Joon Y.Park(2001) have discussed the asymptotic distribution when error series in the AR(1) model yt=yt-1+εtisε1=(?)jut-j,and{u1}is i.i.d, E(u1)= 0,E(u1)2=σ2,E|ut|<∞,r≥4. Zacharias Psaradkis(2001) have discussed the asymptotic distribution when the AR(1) model is yt=yt-1+εt, the error seriesεt is a linear processes.In this paper, we first discuss the approximate critical values for the unit root test when the error series in the AR(p) model is i.i.d, we obtain that when the error series in the AR(p) model is {εt} i.i.d, E(εt)= 0, E(ε1)2=σε2> 0, E(ε14)<∞,the asymptotic distribution is:Second, we consider the asymptotic distribution when the AR(p) model have a drift,and the asymptotic distribution is: Last we consider asymptotic distribution when the error series is a AR progress,we obtian the result: the sieve bootstrap variance of the mean is model-free within a class of reversible linear process.