Generalized continuons-time ARMA processes

广义Ornstein-Uhlenbeck过程是Levy框架内具有指数递减自相关函数的连续时间过程。它们在金融领域被用作随机波动率模型，在保险领域被用作风险模型。连续时间过程特别适合于不规则间隔和高频数据。这类模式在两个方面受到限制。在实际中，金融时间序列往往是具有相依成分的多变量。此外，相关函数不一定是指数递减的。本项目的目的是建立一个多元广义Ornstein-Uhlenbeck模型，并研究该模型的性质。对多元广义Ornstein-Uhlenbeck过程进行扩充，以得到一类灵活的相关结构，从而得到一类广义连续时间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.