  Several large volatility matrix inference procedures have been developed,
based on the latent factor model. They often assumed that there are a few of
common factors, which can account for volatility dynamics. However, several
studies have demonstrated the presence of local factors. In particular, when
analyzing the global stock market, we often observe that nation-specific
factors explain their own country's volatility dynamics. To account for this,
we propose the Double Principal Orthogonal complEment Thresholding
(Double-POET) method, based on multi-level factor models, and also establish
its asymptotic properties. Furthermore, we demonstrate the drawback of using
the regular principal orthogonal component thresholding (POET) when the local
factor structure exists. We also describe the blessing of dimensionality using
Double-POET for local covariance matrix estimation. Finally, we investigate the
performance of the Double-POET estimator in an out-of-sample portfolio
allocation study using international stocks from 20 financial markets.
