Statistical inference for stochastic models

所提出的研究课题是我在随机建模的估计和推理方面的持续研究计划的一个方面。非线性时间序列模型属于Gestival族。我们将研究这些过程的参数识别，估计和诊断工具。此外，我们将研究一个应用程序的投资组合优化。我们还将研究甘精胰岛素在平均过程。投资组合的问题是相当重要的，因为目前的方法假设回报是独立的，往往是正态分布。独立性和正态性假设会使风险度量产生偏差，通常会大大低估风险，例如风险价值。本文将研究在高性能计算（HPC）环境下的空间过程模拟。目前HPC已被应用到确定性的空间功能，但不随机空间过程，一般有一个空间或邻里的相互作用组件。后者不仅对我们的激励应用很重要，而且对许多应用也很重要，例如空间或位置是关键特征的生态和环境应用。我们还将研究使用高阶Ito-Taylor方法、应用于商品石油和天然气市场的周期性Ornstein-Uhlenbeck过程以及多猎物竞争物种模型的扩散估计。前两个扩散应用程序的动机，并将使用实验数据和欧洲天然气商品数据集。

The proposed research topics are aspects of my continuing research program in estimation and inference for stochastic modeling. The nonlinear times series models are of the GARCH family. We will study parameter identification, estimation and diagnostic tools for these processes. In additional we will study an application to portfolio optimization. We will also study GARCH in mean processes. The portfolio question is quite important as the present methodology assumes returns are independent, and often with a normal distribution. Independence and the normality assumptions bias measures of risk and in general greatly underestimates risk, such as value at risk. This method will address this problem.We will study simulation of spatial processes in a high performance computing (HPC) environment. At present HPC has been applied to deterministic spatial functions, but not to stochastic spatial processes, which in general have a spatial or neighbourhood interaction component. The later is important not just for our motivating application, but for many applications, such as ecology and environmental applications where space or location is a key feature.We will also study estimation for diffusions using higher order Ito-Taylor methods, a periodic Ornstein-Uhlenbeck process applied to commodity oil and gas markets, and a multi prey competing species model. The first two diffusion applications are motivated by and will use experimental data and a European natural gas commodity data set.