We propose an approach to model realized covariance matrices by transforming them and selecting only persistent series to model. The proposed models can capture the persistence and the common dynamics in the volatilities and the correlations, while ensuring the positive-definiteness of the covariance matrix and modeling parsimoniously to avoid the curse of dimensionality such that we can deal with a large cross-section of stocks. We use the $\gamma$-transformation of \cite{archakov2021new} to ensure the positive-definiteness of the realized correlation matrix and construct models that exploit the empirical persistence and common dynamics in the $\gamma$-transformed realized correlations. In a forecasting setting we find that modeling a selection of less than 10\% of the transformed realized correlations yields the same the forecasting performance as modeling all the transformed realized correlations for a 1-day-head horizon and that over longer horizons the modeling of the joint dynamics in the realized volatilities and a selection of the realized correlations improves the forecasting significantly.

When factors are weak, covariance-based factor analysis methods tend to exhibit poor performance. To address this issue in the presence of non-Gaussian factors, we propose a novel approach that utilizes the eigenvalue decomposition of the product of higher-order multi-cumulant matrices and their transposes. We derive the asymptotic properties of this Higher-order multi-cumulant Factor Analysis (HFA) within the framework of weak factors that are non-Gaussian and where error terms are Gaussian. Simulation results demonstrate that HFA substantially enhances the accuracy of both factor selection and estimation when compared to traditional covariance-based methods. Additionally, we apply HFA to the FRED-MD dataset, detecting and estimating factors to improve forecasts of the monthly S&P 500 equity premium.

We consider the prediction of the global minimum variance portfolio (GMVP) weights based on realized covariance matrices computed from high-frequency intraday returns of risky assets. As the multivariate high-dimensional time series process of covariance matrices is rather complex and hard to estimate without substantial simplifications of the model structure, there exist various competing approaches for predicting the GMVP weights.

Our major contribution is the development of a novel approach for combining several given GMVP prediction rules in order to determine a low dimensional time-varying vector of these rules' proportions for the GMVP.

We provide statistical results on realized rule proportions and suggest a feasible low-dimensional approach to forecast the proportions based on a set of pre-determined GMVP prediction rules. Our findings are illustrated in an empirical study where we forecast the GMVP weights based on 265 risky assets by combining various popular portfolio rules.