EQUIVALENCE OF TWO EXPRESSIONS OF THE IMPACT MATRIX
证明了Johansen(1995)和Paruolo(1997)与Phillips(1998)中移动平均冲击矩阵两种表达的参数等价性，使研究者可基于任一表达式进行相同的统计推断。
This note gives a proof of the equivalence between two expressions of the moving-average impact matrix; one is given by Johansen (1995, Likelihood-Based Inference in Cointegrated Vector Autoregressive Models ) and Paruolo (1997, Econometric Theory 13, 79–118), and the other appears in Phillips (1998, Journal of Econometrics 83, 21–56) as the limit of the impulse response function. Because these expressions are shown to be parametrically equivalent, we can make the same statistical inference about the impact matrix based on either Johansen (1995) and Paruolo (1997) or Phillips (1998).