Estimation of Large Volatility Matrices with Low-Rank Signal Plus Sparse Noise Structures

In this paper, we propose a parsimonious model to estimate large volatility matrices by combining DCC-GARCH, sparsity-induced weak factors (sWFs) and POET framework in Fan et al. (2013). We call this method the DCC and sWFs extended POET (DCC-ePOET). Built on the mixed factor structures, we estimate volatility matrices through the univariate volatilities of observable factors and weak latent factors with a linear transformation. We further include a sparse noise covariance estimator obtained by an aptivethreshold method proposed in POET to dressthe singularity issue when the cross-sectional dimension N is larger than the sample size T, and capture the weak correlations in the factor models'idiosyncratic terms. Simulation studies show that our proposed method achieves good finite-sample performance. Empirical studies demonstrate that the developed method is superior to several candidates in the analysis of out-of-sample minimum variance portfolio allocations.