基于宏观数据呈现非平稳（单位根）和高维性的基本特征，本项目拟研究：从大型宏观数据集中提取共同非平稳冲击（因子）；将共同非平稳冲击与重要宏观（或金融）变量构建协整模型，进行协整回归的估计与检验，由此实现传统协整模型的理论创新；并通过我国宏观数据集的实证分析，揭示非平稳因子与重要宏观变量的长期均衡关系，由此实现本项目的应用创新。首先，我们拟研究基于极大似然法非平稳因子估计量的渐进性质，并将其与基于主成分分析法估计量进行比较；其次，本项目拟采用完全修正的最小二乘法估计上述协整关系，并研究序列相关性、潜在因子内生性、奇异性和因子估计误差对于协整系数估计量的影响。进一步，我们拟研究基于残差的协整检验统计量在上述设定下的渐近性质。最后，本项目拟收集和构建代表我国宏观经济的非平稳数据集，从中提取共同非平稳冲击，构建其与GDP的协整系统，并运用冲击分解理论对我国的经济增长进行长期趋势分解。

Given the pervasive non-stationarity of large dimensional macroeconomic data, this project considers estimating the common stochastic trends (latent nonstationary factors) from large panel data; estimating and testing cointegration between an integrated series of interest and the estimated latent factors. This extension of traditional cointegration analysis into the high dimensional framework will highlight a theoretical breakthrough. Based on the theoretical results, we will apply our method to the large panel data of China’s macroeconomy, study the long run equilibrium relation between some crucial macroeconomic variables and the latent common factors, to highlight an empirical analysis innovation. More specifically, (1) We propose a method based on Maximum Likelihood to estimate the latent nonstationary factors, and compare with estimator based on the principal component analysis; (2) Using estimated factors as the regressor, we will use the fully modified least squares (FM-OLS) regressions to account for potential serial correlation, endogeneity, singularity, and estimation error of latent factors in the cointegration regression; (3) Also, we will study the asymptotic properties of the residual-based cointegration test statistics with estimated latent factors; (4) Lastly, we will collect and construct a large nonstationary panel data for China’s macroeconomy, estimate the common stochastic trends in the panel, and estimate and test the cointegration between GDP and the latent factors. The cointegration system made of GDP and the estimated latent factors can serve as a base model for the identification of long-run and short-run shocks of GDP and for the decomposition of the long-run trends of economic growth.