enhanced by several papers such as [@TWZ2013; @KWZ2016; @KKLW2018]. Meanwhile, such methods require a kind of sparsity of the target quadratic covariation matrix itself, which seems unrealistic in financial data in view of the celebrated factor structure such as the Fama-French three-factor model of [@3factor]. To overcome this issue, @FFX2016 have proposed a covariance estimation method based on a continuous-time (approximate) factor model with observable factors, which can be seen as a continuous-time counterpart of the method introduced in @FLM2011. The method has been further extended in various directions such as situations with unobservable factor, noisy and non-synchronous observations, heavy-tail errors and so on; see [@AX2017; @DLX2017; @KLW2017; @FK2017; @Pelger2019] for details. As an alternative approach to avoid assuming the sparsity of the target matrix itself, @BNS2018 have proposed applying the graphical Lasso, which imposes the sparsity on the inverse of the target matrix rather than the target matrix itself. On the empirical side, high-dimensional covariance matrix estimation from high-frequency financial data is particularly interesting in portfolio allocation. We refer to [@Ubukata2010; @FLY2012; @LSS2016] for illustrations of relevant empirical work on this topic, in addition to the empirical results reported in the papers cited above. 0 Additionally, it would be 