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Based on a General Dynamic Factor Model with infinite-dimensional factor space, we develop a new estimation and forecasting procedures for conditional covariance matrices in high-dimensional time series. The performance of our approach is evaluated via Monte Carlo experiments, outperforming many alternative methods. The new procedure is used to construct minimum variance portfolios for a high-dimensional panel of assets. The results are shown to achieve better out-of-sample portfolio performance than alternative existing procedures.

Forecasting Conditional Covariance Matrices in High-Dimensional Time Series: A General Dynamic Factor Approach