Quantile factor analysis for large-dimensional time series with statistical guarantee

Quantile is an important measure in finance and quality assessment in service industry. In this paper, we model the temporal and cross-sectional interactive effect of the quantiles of large-dimensional time series by a latent quantile factor model. The factor loadings and scores are learnt with statistical guarantee via an iterative check-loss-minimization procedure. Without any moment constraint on the idiosyncratic errors, we correctly identify the common and idiosyncratic components for each variable. We obtained the statistical convergence rates of the minimization estimators. Bahardur representations for the estimated factor loadings and scores are provided under some mild conditions. Moreover, a robust method is proposed to select the number of factors consistently. Simulation experiments checked the validity of the theory. Our analysis on a financial data set shows the superiority of learning quantile factors in portfolio allocation over other state-of-the-art methods that learn mean factors.