Collaborative Research: Applied Probability and Time Series Modeling

将对Levy驱动的CARMA(连续时间ARMA)过程的性质进行研究，并开发有效的推理方法。所得结果将被用于研究具有Levy驱动的CARMA波动率的随机波动率模型和进一步研究COGARCH模型。参数在“变点”之间的时间间隔内不变的时间序列是一类重要的非平稳时间序列，已被发现在水文学、地震学和金融学中特别有用。基于最小化模型最小描述长度的新估计技术的性质和应用将被开发和推广，以涵盖具有各种类型的结构突变的一般类型的过程，该模型包括变点的数目及其位置作为参数。还将开发用于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，将应用于非因果或不可逆ARMA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15年中，人们普遍认为需要开发新的模型和技术来分析科学、工程、生物医学和金融应用中的时间序列数据。这些新模型所要求的一些特征是非线性、复杂的相依结构、强偏离正态分布和非平稳性。目前的提案满足了这些需求。它寻求加强对模型所代表的物理和经济过程的理解。开发有效的估计和模拟技术将是这项研究的重要组成部分。

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.