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 , the negative part , and the mixed part . DRD decomposition is applied to to obtain the realized volatility matrix and the realized correlation matrix . We then use a deep learning long short‐term memory (LSTM) model to predict and employ the vector heterogeneous autoregressive (HAR) model to forecast the vectorization of , thereby constructing a predictive model for . The forecasting procedure for the negative part mirrors that for the positive part . The matrix factor (MF) model is utilized to reduce the dimensionality of 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 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. for this paper are available online.