Statistical inference for stochastic models

随机模型的统计推断

• 批准号: 5724-2011
• 负责人: Kulperger, Reginald
• 金额: $ 1.53万
• 依托单位: University of Western Ontario
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=635958
• 关键词: Statistical; inference; stochastic; models

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.

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。非线性时间序列模型属于GARCH族。我们将研究这些过程的参数识别、估计和诊断工具。此外，我们将研究投资组合优化的应用。我们还将研究GARCH在均值过程中的应用。投资组合问题非常重要，因为目前的方法假设收益是独立的，并且通常是正态分布。独立性和正态性假设对风险度量有偏差，并且通常大大低估了风险，例如风险价值。这个方法将解决这个问题。我们将在高性能计算（HPC）环境中研究空间过程的模拟。目前，高性能计算已被应用于确定性空间函数，但尚未应用于随机空间过程，因为随机空间过程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来估计扩散。前两个扩散应用是由实验数据和欧洲天然气商品数据集驱动的。