Forecasting the High-Frequency Covariance Matrix Using the Lstm-Mf Model

Accurate prediction of high-dimensional covariance matrices is crucial for portfolio and risk management. In the model developed in this work, high-frequency financial data is used to obtain the realized covariance matrix, and the realized semicovariance is used to decompose the covariance matrix into a summation of the positive part Pt, negative part Nt, and mixed part Mt of the realized semicovariance. DRD decomposition is carried out for Pt to obtain the realized volatility matrix Dt+ and the realized correlation matrix Rt+. We construct a deep-learning long short-term memory (LSTM) model to predict Dt+ and use the vector heterogeneous autoregressive (HAR) model to predict the vectorization of Rt+, building a prediction model for Pt. The prediction procedure for the negative part Nt is the same as that for the positive part Pt. The matrix factor (MF) model is used to reduce the dimension of Mt to obtain the factor matrix, and this is predicted using the vector HAR model for the vectorization of factor matrices, constructing the LSTM-MF realized covariance matrix prediction model. Economic evaluation of the covariance prediction model was undertaken using minimum-variance portfolios with and without L1 constriction. The empirical analysis showed that, compared to the other covariance prediction models considered, LSTM-MF achieved a higher prediction accuracy and Sharpe ratio, and its overall effect was the best