Collaborative Research: Applied Probability and Time Series Modeling

合作研究：应用概率和时间序列建模

• 批准号: 1107031
• 负责人: Richard Davis
• 金额: $ 30万
• 依托单位: Columbia University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-06-01 至 2015-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1107031&HistoricalAwards=false
• 关键词: Collaborative; Research; Applied; Probability; Time

An investigation of the properties of Levy-driven CARMA (continuous-time ARMA) processes will be undertaken and efficient methods of inference developed. The results will be applied to the study of stochastic volatility models with Levy-driven CARMA volatility that have applications that go beyond finance to turbulence and some neuroscience processes. Time series in which the parameters are constant over time-intervals between change-points constitute an important class of non-stationary time series which has been found particularly useful in hydrology, seismology, neuroscience, environmental science and finance. Properties and applications of a new estimation technique based on the minimization of the minimum description length of a model that includes the number of change-points and their locations as parameters will be developed and extended to cover a general class of processes with structural breaks. It is hoped that this technique can also be adapted for detection of both additive and innovational outliers. Linear and nonlinear models for multivariate time series, with a view towards modeling temporal brain dynamics, will also play a major role in this research proposal. These models include a mixture of possibly nonlinear vector autoregressions and a class of not necessarily causal vector autoregressions. The latter class, although linear, exhibits features previously only associated with nonlinear models and allows for the possibility of foresight in the sense of dependence of one or more components of future shocks. In the last fifteen years, 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, financial, and neuroscience applications. Some of the features required of these new models are nonlinearity, complex dependence structures, strong deviations from normality and non-stationarity. In neuroscience, environmental and financial modeling there is also a demand for continuous-time models which incorporate these features. The current proposal addresses these needs. It seeks to enhance understanding of the physical, biomedical, and economic processes represented by the models. The development of efficient estimation and simulation techniques will be an essential component of the research.

将对征收驱动的Carma（连续时间ARMA）过程的性质进行研究，并开发了有效的推理方法。结果将应用于具有征收驱动的Carma波动性的随机波动率模型的研究，该模型的应用超出了财务上的湍流和某些神经科学过程。 在变化点之间的参数持续时间间隔的时间序列构成了一个重要类别的非平稳时间序列，在水文，地震学，神经科学，环境科学和金融方面已被发现特别有用。新估计技术的属性和应用是基于模型的最小描述长度的最小化，该长度包括变更点的数量及其位置作为参数，并将开发并扩展，以覆盖具有结构性断裂的一般过程。希望该技术也可以适应添加剂和创新异常值。 多元时间序列的线性和非线性模型，以建模时间大脑动力学，也将在该研究建议中起主要作用。这些模型包括可能的非线性矢量自动加工和一类不一定是因果矢量自动加注的混合物。后一类虽然线性虽然表现出以前仅与非线性模型相关联的特征，并且可以在未来冲击的一个或多个组成部分的依赖意义上具有远见。在过去的十五年中，人们对开发新模型和技术的开发需要广泛认可，以分析科学，工程，生物医学，财务和神经科学应用的时间序列数据。 这些新模型所需的某些特征是非线性，复杂的依赖性结构，与正态性和非平稳性的强偏差。 在神经科学中，环境和财务建模也需要连续时模型，以结合这些功能。 当前的提案解决了这些需求。它试图增强对模型代表的物理，生物医学和经济过程的理解。有效估计和仿真技术的发展将是研究的重要组成部分。