基于比值法对高维时间序列因子模型中因子个数的实证分析——以美国宏观经济数据为例
Empirical Analysis of the Number of Factors in High-Dimensional Time Series Factor Models Based on the Ratio Method—Taking US Macroeconomic Data as an Example

经济关系民生，代表一个国家的生产力水平。宏观经济是国家经济的总体表现和指导方向，直接影响着国家的发展和稳定。宏观经济数据分析是理解经济运行机制、指导政策制定和实施、支持企业战略规化以及风险管理的重要工具，对于实现经济稳定增长和可持续增长至关重要。本文采用高维时间序列因子模型，对美国宏观经济数据进行降维分析，在ER、CR、TCR、GR四种比值估计器下，估计公共因子的个数。估计结果显示，ER、GR估计器识别出的因子个数为2，CR、TCR估计器识别出的因子个数为3。通过AIC和BIC准则对估计结果进行评估，发现CR、TCR估计器识别出的因子个数结果更为准确，将3个公共因子分别解释为GDP、就业与失业、消费价格指数和信心指数，能够更好地对宏观经济数据进行解释，进而了解国家的经济状况。
The economy directly affects people’s livelihoods and represents a country’s level of productivity. Macroeconomics reflects the overall performance and guides principles of a nation’s economy, directly impacting its development and stability. Analyzing macroeconomic data is a crucial tool for understanding economic mechanisms, guiding policy formulation and implementation, supporting strategic planning for businesses, and managing risks. It is vital for achieving both stable and sustainable economic growth. In this study, a high-dimensional time series factor model is employed to conduct dimensionality reduction analysis on macroeconomic data from the United States. Using four ratio estimators, ER, CR, TCR, and GR, the number of common factors is estimated. The results indicate that the ER and GR estimators identify two common factors, while the CR and TCR estimators identify three. Evaluation based on AIC and BIC criteria suggests that the CR and TCR estimators provide more accurate results in identifying the number of factors. These three common factors are interpreted as GDP, employment and unemployment, and consumer price and confidence indices, offering better insights into macroeconomic data and understanding the country’s economic conditions.