STATISTICAL INFERENCE IN COINTEGRATED VECTOR AUTOREGRESSIVE MODELS WITH NONLINEAR TIME TRENDS IN COINTEGRATING RELATIONS
协整关系含非线性时间趋势的向量自回归模型：统计推断AI 解读 ↓
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协整关系含非线性时间趋势的向量自回归模型：统计推断
- 研究问题
- 协整关系含非线性时间趋势和一般非线性参数约束时，如何分别推断长期关系与短期动态参数，并处理短期参数未识别的情形？
- 方法与思路
- 作者研究高斯最大似然估计及 Wald、拉格朗日乘子和似然比检验的渐近分布，并讨论参数未识别时信息矩阵的估计。
- 材料陈述的贡献
- 摘要称，长期参数估计有混合正态极限，短期参数估计有通常正态极限；相关检验可有卡方极限，证明无需似然二阶偏导。
- 阅读关注点
- 应核对长期与短期推断各自的识别条件、信息矩阵修正方式，以及无需二阶导数和部分无需干扰参数可微的适用范围。
- 阅读边界
- 仅据所给 Crossref 摘要，不能认为未识别参数本身也能被有效推断；具体条件、自由度及信息矩阵构造均需查阅全文。
原文摘要
This paper continues the work of Saikkonen (2001, Econometric Theory 17, 296–326) and develops an asymptotic theory of statistical inference in cointegrated vector autoregressive models with nonlinear time trends in cointegrating relations and general nonlinear parameter restrictions. Inference on parameters in cointegrating relations and short-run dynamics is studied separately. It is shown that Gaussian maximum likelihood estimators of parameters in cointegrating relations have mixed normal limiting distributions and that related Wald, Lagrange multiplier, and likelihood ratio tests for general nonlinear hypotheses have usual asymptotic chi-square distributions. These results are shown to hold even if parameters in the short-run dynamics are not identified. In that case suitable estimators of the information matrix have to be used to justify the application of Wald and Lagrange multiplier tests, whereas the likelihood ratio test is free of this difficulty. Similar results are also obtained when inference on parameters in the short-run dynamics is studied, although then Gaussian maximum likelihood estimators have usual normal limiting distributions. All results of the paper are proved without assuming existence of second partial derivatives of the likelihood function, and in some cases even differentiability with respect to nuisance parameters is not required.