Applied Probability and Time Series Modelling

DMS-0308109PI：Peter J.Brockwell标题：应用概率和时间序列建模摘要：研究Levy驱动的线性和非线性连续时间自回归-滑动平均(ARMA)过程的性质及其在金融中的应用。还将讨论有关非线性连续时间模型的定常解的存在性以及离散时间模型与其连续时间类似物之间的关系的问题。在离散时间中，将研究广义线性ARMA模型的随机稳定性，以期对计数的时间序列进行建模。对于这些模型和由非高斯噪声驱动的全通模型，将开发有效的估计技术。后一过程的结果将应用于非因果和/或不可逆ARMA模型的识别和估计问题。在过去的十年里，人们普遍认识到需要开发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的时间序列数据。导致这一需求的主要特征包括非线性、复杂的相关性结构和强烈的正态偏离，离散值数据出现在许多遗传和生物医学应用中。在金融应用中，需要具有这些特征的连续时间模型。该提案解决了这些需求，目的是加强对模型所代表的物理和经济过程的科学理解。

DMS-0308109PI: Peter J. BrockwellTitle: Applied probability and Time Series modeling Abstract:Properties and applications in finance of Levy-driven linear and non-linear continuous-time autoregressive-moving average (ARMA) processes will be investigated. Questions concerning existence of stationary solutions for non-linear continuous-time models and relations between discrete-time models and their continuous-time analogues will also be addressed. In discrete time, the stochastic stability of generalized linear versions of ARMA models will be studied with a view to modeling time series of counts. Efficient estimation techniques for these models and for all-pass models driven by non-Gaussian noise will be developed. The results for the latter processes will be applied to the problem of identification and estimation for non-causal and/or non-invertible ARMA models. In the last decade 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. Major features giving rise to this need include non-linearity, complex dependence structures and strong deviations from normality, with discrete-valued data arising in many genetic and biomedical applications. In financial applications there is a need for continuous-time models exhibiting these characteristics. The proposal addresses these needs, with the goal of enhancing scientific understanding of the physic and economic processes represented by the models.