A Stastistical Analysis of Cointegration for I(2) Variables
研究了VAR模型中I(2)变量的推断方法，提出两步降秩回归估计，证明估计量渐近分布为混合高斯，可用卡方分布进行推断，并给出了I(2)变量存在的多元检验，用英国价格、利率和汇率数据演示。
This paper discusses inference for I(2) variables in a VAR model. The estimation procedure suggested consists of two reduced rank regressions. The asymptotic distribution of the proposed estimators of the cointegrating coefficients is mixed Gaussian, which implies that asymptotic inference can be conducted using the χ 2 distribution. It is shown to what extent inference on the cointegration ranks can be conducted using the tables already prepared for the analysis of cointegration of I(1) variables. New tables are needed for the test statistics to control the size of the tests. This paper contains a multivariate test for the existence of I(2) variables. This test is illustrated using a data set consisting of U.K. and foreign prices and interest rates as well as the exchange rate.