Circularly Projected Common Factors for Grouped Data
针对分组数据提取共同因子时迭代PCA耗时、CCA只能处理两组数据的问题，提出了两种无需迭代、计算高效的循环投影方法，可统一估计多组数据的共同因子，并应用于国际商业周期和零售价格联动研究。
To extract the common factors from grouped data, multilevel factor models have been put forward in the literature, and methods based on iterative principal component analysis (PCA) and canonical correlation analysis (CCA) have been proposed for estimation purpose. While iterative PCA requires iteration and is hence time-consuming, CCA can only deal with two groups of data. Herein, we develop two new methods to address these problems. We first extract the factors within groups and then project the estimated group factors into the space spanned by them in a circular manner. We propose two projection processes to estimate the common factors and determine the number of them. The new methods do not require iteration and are thus computationally efficient. They can estimate the common factors for multiple groups of data in a uniform way, regardless of whether the number of groups is large or small. They not only overcome the drawbacks of CCA but also nest the CCA method as a special case. Finally, we theoretically and numerically study the consistency properties of these new methods and apply them to studying international business cycles and the comovements of retail prices.