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Several large volatility matrix inference procedures have been developed,based on the latent factor model. They often assumed that there are a few ofcommon factors, which can account for volatility dynamics. However, severalstudies have demonstrated the presence of local factors. In particular, whenanalyzing the global stock market, we often observe that nation-specificfactors 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 establishits asymptotic properties. Furthermore, we demonstrate the drawback of usingthe regular principal orthogonal component thresholding (POET) when the localfactor structure exists. We also describe the blessing of dimensionality usingDouble-POET for local covariance matrix estimation. Finally, we investigate theperformance of the Double-POET estimator in an out-of-sample portfolioallocation study using international stocks from 20 financial markets.

Large Volatility Matrix Analysis Using Global and National Factor Models