THE INTEGRATION ORDER OF VECTOR AUTOREGRESSIVE PROCESSES
证明了向量自回归过程的积分阶数等于特征方程中单位根的重数与伴随矩阵多项式中单位根的重数之差，并与标准I(1)和I(2)条件等价。
We show that the order of integration of a vector autoregressive process is equal to the difference between the multiplicity of the unit root in the characteristic equation and the multiplicity of the unit root in the adjoint matrix polynomial. The equivalence with the standard I(1) and I(2) conditions (Johansen, 1996, Likelihood-Based Inference in Cointegrated Vector Auto-Regressive Models) is proved.I am very grateful to Søren Johansen for his precious insights and his continuous help throughout the development of the paper. I also thank Paolo Paruolo (the coeditor) and the referees for valuable feedback. This paper was written while the author was a Post Doc at the Department of Economics, University of Copenhagen, and the hospitality of this institution is gratefully acknowledged.