标题： 广义 Wishart 过程 显示英文标题

标题： Generalised Wishart Processes

摘要： 我们引入了一个具有Wishart边缘分布的随机过程：广义Wishart过程（GWP）。它是一组由任意依赖变量索引的半正定随机矩阵的集合。我们用它来建模动态（例如，时变）协方差矩阵。与现有模型不同，它可以捕捉多种类别的协方差结构，可以轻松处理缺失数据，依赖变量可以轻松包含除时间以外的协变量，并且随着维度的增长表现良好；无需自由参数，可选参数也易于解释。我们描述了如何构造GWP，介绍了推理和预测的一般程序，并表明它在金融数据上甚至优于其主要竞争对手多元GARCH。我们还展示了如何在考虑动态相关性的同时预测多元过程的均值。 显示英文摘要

摘要： We introduce a stochastic process with Wishart marginals: the generalised Wishart process (GWP). It is a collection of positive semi-definite random matrices indexed by any arbitrary dependent variable. We use it to model dynamic (e.g. time varying) covariance matrices. Unlike existing models, it can capture a diverse class of covariance structures, it can easily handle missing data, the dependent variable can readily include covariates other than time, and it scales well with dimension; there is no need for free parameters, and optional parameters are easy to interpret. We describe how to construct the GWP, introduce general procedures for inference and predictions, and show that it outperforms its main competitor, multivariate GARCH, even on financial data that especially suits GARCH. We also show how to predict the mean of a multivariate process while accounting for dynamic correlations.