Collaborative Research: Applied Probability and Time Series Modeling

Levy驱动的CARMA（连续时间阿尔马）过程的性质的调查将进行和有效的推理方法的发展。研究结果将被应用于随机波动模型与利维驱动的CARMA波动，有超越金融动荡和一些神经科学过程的应用程序的研究。在变点之间的时间间隔上参数恒定的时间序列构成了一类重要的非平稳时间序列，在水文学、地震学、神经科学、环境科学和金融学中特别有用。一种新的估计技术的基础上的最小化的最小描述长度的模型，包括变点的数量和它们的位置作为参数的属性和应用程序将被开发和扩展，以涵盖一般类的过程与结构突变。希望这种技术也可以适用于检测添加剂和创新的离群值。多元时间序列的线性和非线性模型，以模拟时间大脑动力学，也将在这项研究中发挥重要作用。这些模型包括可能的非线性向量自回归和一类不一定是因果向量自回归的混合。后一类虽然是线性的，但表现出以前只与非线性模型有关的特征，并允许在未来冲击的一个或多个组成部分的依赖性意义上进行预见。在过去的15年里，人们广泛认识到需要开发新的模型和技术，用于分析来自科学、工程、生物医学、金融和神经科学应用的时间序列数据。这些新模型所需的一些功能是非线性，复杂的依赖结构，从正常和非平稳性的强烈偏差。在神经科学、环境和金融建模中，也需要包含这些特征的连续时间模型。目前的建议满足了这些需要。它旨在加强对模型所代表的物理，生物医学和经济过程的理解。有效的估计和模拟技术的发展将是研究的一个重要组成部分。

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.