Statistical inference for stochastic models

提出的研究主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GARCH家族。我们将研究这些过程的参数识别、估计和诊断工具。此外，我们还将研究其在投资组合优化中的应用。我们还将研究均值过程中的GARCH。投资组合问题相当重要，因为目前的方法假设收益是独立的，而且通常是正态分布的。独立性和正态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。这种方法将解决这个问题。我们将研究在高性能计算(HPC)环境下的空间过程模拟。目前，HPC已被应用于确定性空间函数，但不适用于随机空间过程，后者通常具有空间或邻域相互作用成分。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学和环境应用。我们还将研究使用高阶Ito-Taylor方法估计扩散，应用于商品石油和天然气市场的周期Ornstein-Uhlenbeck过程，以及多食饵竞争物种模型。前两个扩散应用是由实验数据和欧洲天然气商品数据集推动的，并将使用这些数据。

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.