The paper develops a novel realized matrix-exponential stochastic volatility model of multivariate returns and realized covariances that incorporates asymmetry and long memory (hereafter the RMESV-ALM model), and higher-moment spillovers. The matrix exponential transformation guarantees the positive definiteness of the dynamic covariance matrix. We decompose the likelihood function of the RMESV-ALM model into two components: one based on the conventional Kalman filter, and the other evaluated by a Monte Carlo likelihood technique. We consider a two-step quasi-maximum likelihood estimator for maximizing the likelihood function, and examine the finite sample properties of the estimator. The specification enables us to analyze asymmetric and higher-moment spillover effects in the covariance dynamics via news impact curves and impulse response functions. Using high frequency data for three US financial assets, the new model is estimated and evaluated. The forecasting performance of the new model is compared with a novel dynamic realized matrix-exponential conditional covariance model. Our empirical results suggest the RMESV-ALE specification to be superior, and spillover effects are found from returns or volatility to the remaining volatilities.

本文开发了一种新的实现矩阵-指数随机波动率模型，该模型包含了不对称性和长记忆（以下称为 RMESV-ALM 模型）和更高矩溢出的多元收益和实现协方差。矩阵指数变换保证了动态协方差矩阵的正定性。我们将 RMESV-ALM 模型的似然函数分解为两个部分：一个基于传统的卡尔曼滤波器，另一个通过蒙特卡洛似然技术进行评估。我们考虑一个用于最大化似然函数的两步准最大似然估计器，并检查估计器的有限样本属性。该规范使我们能够通过新闻影响曲线和脉冲响应函数分析协方差动态中的不对称和更高矩溢出效应。使用三种美国金融资产的高频数据，对新模型进行估计和评估。将新模型的预测性能与新的动态实现矩阵-指数条件协方差模型进行了比较。我们的实证结果表明，RMESV-ALE 规范更为优越，并且从回报或波动率对剩余波动率的溢出效应中发现。