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。所得结果将应用于Levy驱动的CARMA波动率随机波动率模型的研究以及COGARCH模型的进一步研究。参数在"变点“之间的时间间隔内保持不变的时间序列是一类重要的非平稳时间序列，在水文学、地震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，以涵盖一个一般类的各种类型的结构中断的过程。还将开发由非高斯噪声驱动的全通模型的估计技术。 这些技术，包括最大似然估计和最小离差估计，将被应用于非因果或非可逆阿尔马模型的识别和估计问题。将探索有效估计这类模型的自适应技术。在过去的十五年里，人们广泛认识到需要发展新的模型和技术来分析来自科学、工程、生物医学和金融应用。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。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 and to the further study of COGARCH models. 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 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 of various types. Estimation techniques for all-pass models driven by non-Gaussian noise will also be developed. These techniques, including maximum likelihood and minimum dispersion estimation, will be applied to the problem of identification and estimation for non-causal or non-invertible ARMA models.Adaptive techniques for efficient estimation of such models will be explored.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, and financial applications. Some of the features required of these new models are nonlinearity, complex dependence structures, strong deviations from normality and non-stationarity. The current proposal addresses these needs. It seeks to enhance understanding of the physical and economic processes represented by the models. The development of efficient estimation and simulation techniques will be an essential component of the research.