Based on a General Dynamic Factor Model with infinite-dimensional factor space and MGARCH volatility models, we develop new estimation and forecasting procedures for conditional covariance matrices in high-dimensional time series. The finite-sample performance of our approach is evaluated via Monte Carlo experiments and outperforms most alternative methods. This new approach is also used to construct minimum one-step-ahead variance portfolios for a high-dimensional panel of assets. The results

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... re shown to match the results of recent proposals by Engle et al. (2019) and De Nard et al. (2021) and achieve better out-of-sample portfolio performance than alternative procedures proposed in the literature.