内生性问题下非平稳时间序列间共趋势关系的估计和检验

与传统的协整关系相比，共趋势关系在更为一般的情形下定义了非平稳时间序列间长期稳定的均衡关系。然而，模型中可能存在的内生性问题却极大地阻碍了我们对共趋势关系进行正确的估计和检验。同时，现有统计检验方法在有限样本下很难准确给出非平稳时间序列中趋势成分的具体形式。因此，本课题拟在含有内生性问题且趋势形式不确定的情况下，构建共趋势关系的估计方法和检验理论，从而为在实证中建立内生共趋势关系提供计量理论支持。基于趋势的表示理论，我们提出利用时间的Legendre正交多项式作为天然的工具变量，通过两阶段最小二乘法来得到共趋势系数无偏一致的估计量，并借由相应的Sargan检验来判断共趋势关系是否显著存在。我们的主要任务是推导所构建的估计量和检验统计量的大样本性质，并通过数值模拟研究其有限样本性质。此外，我们拟将内生共趋势理论运用到气候变化领域，来研究全球年平均气温和温室气体排放量之间的共趋势关系。

When compared to the traditional co-integration relationship, the co-trending relationship defines the long-run stable equilibrium between nonstationary time series in a broader sense. However, the problem of endogeneity, which could possibly occur in practice, may greatly affect the correction estimation and testing of the co-trending relationship. Meanwhile, current statistical tools can hardly distinguish between different trend patterns in finite sample cases. Therefore, in this project, we plan to propose estimation and testing theories for the co-trending relationship between nonstationary time series with endogeneity, and this could serve as a theoretical support for empirical researchers who would like to establish co-trending relationship in practice. Based on the representation theories for trends, we propose using Legendre polynomials of time as instrumental variables, and establish unbiased and consistent two-stage least squares estimators for the co-trending coefficients. Meanwhile, the corresponding Sargan-type test could work as a statistical test for the existence of co-trending relationship. Our main objectives include developing the large sample statistical theories and examine the finite sample performance of the estimators and test statistics. In addition, we would also like to apply our model and methods to study the co-trending relationship between global mean temperatures and emissions of greenhouse gases in the science of climate change as an empirical example.