UNIT ROOT TESTING FOR FUNCTIONALS OF LINEAR PROCESSES
研究了误差为线性过程的非线性变换时的单位根检验问题，发现当线性过程具有长记忆性时，渐近分布是Hermite过程的泛函，与经典布朗运动泛函结果显著不同。
We consider the unit root testing problem with errors being nonlinear transforms of linear processes. When the linear processes are long-range dependent, the asymptotic distributions in the unit root testing problem are shown to be functionals of Hermite processes. Functional limit theorems for nonlinear transforms of linear processes are established. The obtained results differ sharply from the classical cases where asymptotic distributions are functionals of Brownian motions.The author thanks the referee and Professor B. Hansen for their valuable suggestions. The work is supported in part by NSF grant DMS-04478704.