Likelihood-Based Inference for Weak Exogeneity in I (2) Cointegrated VAR Models
研究了I(2)协整向量自回归模型中弱外生性的似然推断，推导了条件最大似然估计的渐近性质，证明似然比检验统计量渐近服从卡方分布，并用日本宏观数据做了实证。
This article develops limit theory for likelihood analysis of weak exogeneity in I(2) cointegrated vector autoregressive (VAR) models incorporating deterministic terms. Conditions for weak exogeneity in I(2) VAR models are reviewed, and the asymptotic properties of conditional maximum likelihood estimators and a likelihood-based weak exogeneity test are then investigated. It is demonstrated that weak exogeneity in I(2) VAR models allows us to conduct asymptotic conditional inference based on mixed Gaussian distributions. It is then proved that a log-likelihood ratio test statistic for weak exogeneity in I(2) VAR models is asymptotically χ2 distributed. The article also presents an empirical illustration of the proposed test for weak exogeneity using Japan's macroeconomic data.