Canonical Correlation-based Model Selection for the Multilevel Factors

A great deal of research e ort has been devoted to the analysis of the multilevel factor model. To date, however, limited progress has been made on the development of coherent inference for identifying the number of the global factors. We propose a novel approach based on the canonical correlation analysis to identify the number of the global factors. We develop the canonical correlations di erence (CCD), which is constructed by the di erence between the cross group-averages of the adjacent canonical correlations between factors. We prove that CCD is a consistent selection criterion. Via Monte Carlo simulations, we show that CCD always selects the number of global factors correctly even in small samples. Further, CCD outperforms the existing approaches in the presence of serially correlated and weakly cross-sectionally correlated idiosyncratic errors as well as the correlated local factors. Finally, we demonstrate the utility of our framework with an application to the multilevel asset pricing model for the stock return data of 12 industries in the U.S.