非线性因子模型：估计、检验与应用

Factor models provide a flexible way to summarize and extract information from large data sets and have received extensive attention in economic and financial analysis. In the conventional factor models, the factor loadings, which capture the relationships between economic and financial variables and the latent common factors, are usually assumed to be time invariant. In fact, the relationship among variables undergoes structural changes, possibly due to regime switch, technology progress. To capture this nonlinear feature, this project plans to introduce several nonlinear factor models, and consider the estimation, testing and applications of these models. Firstly, the project will introduce time varying factor models, and propose a local principal component method to estimate the latent factors and the time-varying factor loadings simultaneously; secondly, several methods to determine the number of common factors, robust to structural changes in factor loadings, will also be proposed; thirdly, several consistent tests will be developed to detect the smooth structural changes or structural breaks in factor loadings; fourthly, a time varying factor forecasting model will be proposed to predict the key economic and financial variables under the framework of high-dimensional dataset and nonlinearity; fifthly, a markov regime switching mixed-frequency factor model will be introduced to measure the business cycle, financial cycle and stock market’s cycle as well as their relationship; finally, measures on the economic situation, the central bank's monetary policy reaction function, and so on, will also be developed based on the information summarized by the common factors. The proposed research will not only contribute to the development of econometric modeling and testing, but also provide reasonable tools for empirical applications under the background of big data, which should further facilitate in deriving reliable conclusions and policy recommendations.

因子模型可用少数公因子概括大量数据涵盖的主要信息，在经济金融分析中得到了广泛关注。现有多数因子模型假设因子载荷阵是恒定不变的。事实上，受制度变迁、技术进步等因素的影响，变量之间的影响关系大多存在结构变化。为了刻画这种结构变化，本研究拟提出非线性因子模型，探讨其估计、检验和应用问题。具体研究内容包括：一是提出时变因子模型，并借助非参数方法和主成分分析，估计公因子和时变因子载荷阵；二是提出对结构变化稳健的公因子个数选择方法；三是构造一系列检验统计量，考察因子载荷阵是否存在结构变化；四是构造时变因子预测模型，在大数据和非线性范畴下预测我国关键经济金融指标；五是构建马尔科夫转移混频因子模型，刻画经济周期、金融周期与股市周期的联动效应；六是借助因子模型提取有效信息，测度我国经济运行态势、央行货币政策反应函数等。本研究不仅有助于推动计量方法的发展，而且有助于在大数据环境下构建恰当的实证模型。

因子模型可用少数公因子概括大量数据涵盖的主要信息，从而在经济金融分析中得到了广泛关注。现有大多数因子模型假设因子载荷阵是不随时间变化的。事实上，受制度变迁、技术进步等因素的影响，变量之间的影响关系大多存在结构变化。为了刻画这种结构变化，本研究提出了非线性因子模型和非线性FAVAR模型，探讨其估计、检验和应用问题。目前已取得的研究成果包括：一是基于非参数回归和离散傅里叶变换，从时域和频域角度提出了一系列统计量考察因子模型中的因子载荷阵是否存在结构变动；二是构建了时变FAVAR模型以及函数系数FAVAR模型，基于非参数估计和主成分分析，得到公因子、因子载荷阵和VAR回归系数的一致估计量，并且探讨其结构变化的检验问题；三是基于特征函数、离散傅里叶变换和非参数估计的优良性质，构造了一系列统计量考察分布函数中的结构变化问题、时间序列模型中的结构变化问题以及严平稳假设的检验问题；四是提出了时变系数模型、时变因子模型中有关时变设定形式的检验统计量；五是在理论研究的基础上，借助因子模型考察了我国宏观经济监测和即时预测等问题，并且基于多个关键宏观经济变量的预测误差，构建了宏观经济意外指数和不确定性指数。在理论上，本研究提供了更优良的检验统计量和更丰富的因子模型形式，有助于推动非线性计量建模和检验方法的发展；在实证研究上，本研究采用的混频模型能够更及时准确地预测关键宏观经济指标，从而为决策者制定恰当的经济政策提供理论依据，为我国学者考察不确定性对宏观经济运行的影响提供了数据支持。

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