高频数据下基于LSTM的协方差矩阵预测模型

协方差矩阵的建模与预测,对于金融风险管理、投资组合管理等至关重要。 针对时间序列模型 对高维变量预测精度较低的问题,利用长短记忆神经网络模型(LSTM),提出了基于深度学习的高频数据已 实现协方差矩阵预测模型。 利用金融高频数据得到已实现协方差矩阵,对其进行 DRD 分解,针对相关系数 矩阵 R 进行向量化处理,利用向量异质自回归模型(HAR)预测已实现相关系数矩阵 R;针对已实现波动率 矩阵 D,利用半协方差(semi covariance)思想,结合 LSTM 模型,得到已实现波动率矩阵 D 的深度学习预测模 型,构建了 LSTM-SDRD-HAR 已实现协方差矩阵动态预测模型。 LSTM 模型和 HAR 模型能捕捉实际数据 的长期记忆性,半协方差有利于捕捉金融数据的杠杆性。 实证分析表明:相较于传统向量 HAR 已实现协方 差矩阵预测模型,LSTM-SDRD-HAR 预测已实现协方差矩阵更为准确,基于 LSTM-SDRD-HAR 预测已实现 协方差矩阵构造的有效前沿组合投资效果更佳。

Covariance Matrix Prediction Model Based on LSTM Using High Frequency Data

The modeling and prediction of the covariance matrix is very important for financial risk management and investment portfolio management. To solve the problem of low prediction accuracy of time series models for highdimensional variables long short memory neural network model LSTM is used to propose a covariance matrix prediction model using high-frequency data based on deep learning. The model uses financial high-frequency data to obtain the realized covariance matrix performs DRD decomposition on the realized covariance matrix vectorizes the correlation coefficient matrix R and uses the vector heterogeneous autoregressive model HAR to predict the realized correlation coefficient matrix R. Based on the realized volatility matrix D this paper uses the idea of semi covariance combined with the LSTM model obtains the deep learning prediction model of the realized volatility matrix D and constructs the dynamic prediction model of realized covariance matrix LSTM-SDRD-HAR. The LSTM and HAR model can capture the long-term memory of actual data and the semi-covariance is conducive to capturing the leverage of financial data. The empirical analysis shows that compared with the traditional vector HAR prediction model LSTM-SDRD-HAR has a more accurate prediction of the realized covariance matrix. The effective frontier portfolio investment structured by LSTM-SDRD-HAR prediction is better.