Forecasting the High‐Frequency Covariance Matrix Using the LSTM‐MF Model

Accurate forecasting of high‐dimensional covariance matrices is essential for portfolio and risk management. In this paper, we utilize high‐frequency financial data to obtain a realized covariance matrix. Realized semicovariance is employed to decompose the covariance matrix into three components: the positive part Pt, the negative part Nt, and the mixed part Mt. DRD decomposition is applied to Pt to obtain the realized volatility matrix Dt+ and the realized correlation matrix Rt+. We then use a deep learning long short‐term memory (LSTM) model to predict Dt+ and employ the vector heterogeneous autoregressive (HAR) model to forecast the vectorization of Rt+, thereby constructing a predictive model for Pt. The forecasting procedure for the negative part Nt mirrors that for the positive part Pt. The matrix factor (MF) model is utilized to reduce the dimensionality of Mt and obtain a factor matrix, which is then predicted using the vector HAR model for the vectorization of factor matrices, thus constructing the LSTM‐MF realized covariance matrix prediction model. Economic evaluation of the covariance prediction model is conducted using minimum‐variance portfolios with and without L1 constraint. Empirical analysis demonstrates that, compared with other covariance prediction models considered, the LSTM‐MF model achieves superior prediction accuracy and a higher Sharpe ratio, indicating its overall effectiveness. Supporting Information for this paper are available online.