Applied Probability and Time Series Modelling

应用概率和时间序列建模

• 批准号: 0308109
• 负责人: Peter Brockwell
• 金额: $ 44.99万
• 依托单位: Colorado State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-06-01 至 2007-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0308109&HistoricalAwards=false
• 关键词: Applied; Probability; Time; Series; Modelling

DMS-0308109PI: Peter J. BrockwellTitle: Applied probability and Time Series modeling Abstract:Properties and applications in finance of Levy-driven linear and non-linear continuous-time autoregressive-moving average (ARMA) processes will be investigated. Questions concerning existence of stationary solutions for non-linear continuous-time models and relations between discrete-time models and their continuous-time analogues will also be addressed. In discrete time, the stochastic stability of generalized linear versions of ARMA models will be studied with a view to modeling time series of counts. Efficient estimation techniques for these models and for all-pass models driven by non-Gaussian noise will be developed. The results for the latter processes will be applied to the problem of identification and estimation for non-causal and/or non-invertible ARMA models. In the last decade there has been a widely recognized need for the development of new models and techniques for the analysis of time-series data from scientific, engineering, biomedical and financial applications. Major features giving rise to this need include non-linearity, complex dependence structures and strong deviations from normality, with discrete-valued data arising in many genetic and biomedical applications. In financial applications there is a need for continuous-time models exhibiting these characteristics. The proposal addresses these needs, with the goal of enhancing scientific understanding of the physic and economic processes represented by the models.

DMS-0308109 PI：彼得J.布罗克韦尔标题：应用概率和时间序列建模摘要：性质和应用在金融利维驱动的线性和非线性连续时间自回归移动平均（阿尔马）过程将进行研究。 关于非线性连续时间模型的定态解的存在性以及离散时间模型与其连续时间类似物之间的关系的问题也将得到解决。 在离散时间，广义线性版本的阿尔马模型的随机稳定性将研究，以期建立时间序列的计数。 将开发用于这些模型和由非高斯噪声驱动的全通模型的有效估计技术。 后一个过程的结果将被应用到非因果和/或不可逆的阿尔马模型的识别和估计的问题。在过去十年中，人们普遍认识到需要开发新的模型和技术，用于分析科学、工程、生物医学和金融应用中的时间序列数据。 引起这种需要的主要特征包括非线性、复杂的依赖结构和与正态性的强烈偏离，以及在许多遗传和生物医学应用中产生的离散值数据。 在金融应用中，需要表现出这些特征的连续时间模型。 该提案满足了这些需求，目的是加强对模型所代表的生态和经济过程的科学理解。