Abstract Time series of realized covariance matrices can be modeled in the conditional autoregressive Wishart model family via dynamic correlations or via dynamic covariances. Extended parameterizations of these models are proposed, which imply a specific and time-varying impact parameter of the lagged realized covariance (or correlation) on the next conditional covariance (or correlation) of each asset pair. The proposed extensions guarantee the positive definiteness of the conditional covariance or correlation matrix with simple parametric restrictions, while keeping the number of parameters fixed or linear with respect to the number of assets. Two empirical studies reveal that the extended models have superior forecasting performances than their simpler versions and benchmark models.

中文翻译：

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建模实现的协方差矩阵：一类 Hadamard 指数模型

摘要 已实现协方差矩阵的时间序列可以通过动态相关或动态协方差在条件自回归 Wishart 模型族中建模。提出了这些模型的扩展参数化，这意味着滞后已实现协方差（或相关性）对每个资产对的下一个条件协方差（或相关性）的特定且随时间变化的影响参数。建议的扩展通过简单的参数限制保证条件协方差或相关矩阵的正定性，同时保持参数数量相对于资产数量固定或线性。两项实证研究表明，扩展模型比其简单版本和基准模型具有更好的预测性能。