Generalized continuons-time ARMA processes

广义 Ornstein-Uhlenbeck 过程是 Levy 框架内的连续时间过程，具有指数递减的自相关函数。它们在金融中用作随机波动模型，在保险中用作风险模型。连续时间过程特别适合不规则间隔和高频数据的模型。这种模型在两个方面受到限制。在实践中，金融时间序列通常是具有相关成分的多元变量。此外，相关函数不一定呈指数递减。该项目的目的是开发一个多元广义 Ornstein-Uhlenbeck 模型并研究该模型的属性。应丰富多元广义 Ornstein-Uhlenbeck 过程，以允许一类灵活的依赖结构，从而产生一类广义连续时间 ARMA 过程。

Generalized Ornstein-Uhlenbeck processes are continuous-time processes within a Levy framework having an exponentially decreasing autocorrelation function. They are applied as stochastic volatility models in finance and as risk models in insurance. Continuous-time processes are in particular appropriate models for irregularly-spaced and high-frequency data. Such models are limited in two ways. In practice, financial time series are often multivariate with dependent components. Furthermore, the correlation functions are not necessarily exponentially decreasing. The aim of this project is to develop a multivariate generalized Ornstein-Uhlenbeck model and to study the properties of this model. The multivariate generalized Ornstein-Uhlenbeck processes shall be enriched to allow for a class of flexible dependence structures resulting in the class of generalized continuous-time ARMA processes.