Robust Factor Number Specification for Large-dimensional Elliptical Factor Model

The accurate specification of the number of factors is critical to the validity of factor models and the topic almost occupies the central position in factor analysis. Plenty of estimators are available under the restrictive condition that the fourth moments of the factors and idiosyncratic errors are bounded. In this paper we propose efficient and robust estimators for the factor number via considering a more general static Elliptical Factor Model (EFM) framework. We innovatively propose to exploit the multivariate Kendall's tau matrix, which captures the correlation structure of elliptical random vectors. Theoretically we show that the proposed estimators are consistent without exerting any moment condition when both cross-sections N and time dimensions T go to infinity. Simulation study shows that the new estimators perform much better in heavy-tailed data setting while performing comparably with the state-of-the-art methods in the light-tailed Gaussian setting. At last, a real macroeconomic data example is given to illustrate its empirical advantages and usefulness

Large-dimensional Factor Analysis without Moment Constraints

Large-dimensional factor model has drawn much attention in the big-data era, in order to reduce the dimensionality and extract underlying features using a few latent common factors. Conventional methods for estimating the factor model typically requires finite fourth moment of the data, which ignores the effect of heavy-tailedness and thus may result in unrobust or even inconsistent estimation of the factor space and common components. In this paper, we propose to recover the factor space by performing principal component analysis to the spatial Kendall's tau matrix instead of the sample covariance matrix. In a second step, we estimate the factor scores by the ordinary least square (OLS) regression. Theoretically, we show that under the elliptical distribution framework the factor loadings and scores as well as the common components can be estimated consistently without any moment constraint. The convergence rates of the estimated factor loadings, scores and common components are provided. The finite sample performance of the proposed procedure is assessed through thorough simulations. An analysis of a financial data set of asset returns shows the superiority of the proposed method over the classical PCA method