Collaborative Research: Applied Probability and Time Series Modeling

对levy驱动的CARMA（连续时间ARMA）过程的性质进行了调查，并开发了有效的推理方法。研究结果将应用于levy驱动CARMA波动率的随机波动率模型的研究以及COGARCH模型的进一步研究。在“变化点”之间的时间间隔内参数不变的时间序列构成了一类重要的非平稳时间序列，在水文学、地震学和金融学中特别有用。一种基于模型最小描述长度最小化的新估计技术的特性和应用，包括变化点的数量及其作为参数的位置，将被开发和扩展到涵盖具有各种类型的结构断裂的一般类型的过程。非高斯噪声驱动下的全通模型的估计技术也将得到发展。这些技术，包括最大似然估计和最小离散估计，将应用于非因果或非可逆ARMA模型的识别和估计问题。将探讨有效估计这些模型的自适应技术。在过去的15年里，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、复杂的依赖结构、偏离正态性强和非平稳性。当前的提案解决了这些需求。它力求加强对模型所代表的物理和经济过程的理解。开发有效的估算和模拟技术将是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.