Topics in Heavy Tailed Modeling and Long Range Dependence

[704982] Resnick Sidney Resnick和Gennady Samorodnitsky将继续一个围绕重尾模型及其与远程依赖关系的主题组织的研究项目。重尾模型通常意味着无穷方差，因此偏离高斯方法。研究计划的主题包括重尾模型的参数估计和预测，模型选择和确认，以及长距离依赖和重尾之间的相互作用。特别注意的应用领域包括金融和商品市场以及诸如万维网之类的电信通信网。强调概率建模和统计问题。统计问题包括应对非标准数据特征所隐含的方法变化，如长距离依赖性，缺乏矩和相关性，以及不能被线性结构捕获的依赖性。将制定和研究概率模型，试图定性地解释观测到的数据特征。金融市场和宽带数据网络的日益普及使得收集大量数据成为可能。对一些数据的审查揭示了经典统计和概率模型无法处理的特点，因此，本项目具有双重目的：(a)开发统计工具，利用这些数据更可靠地拟合模型并作出预测；(b)建立概率模型，从质量上了解所调查系统的性质。例如，现代宽带网络表现出与经典模型所预测的大不相同的特征。这项研究可能回答的一个问题是，“什么时候向网络增加服务能力在经济上是可取的？”

9704982 Resnick Sidney Resnick and Gennady Samorodnitsky will continue a program of research organized around the theme of heavy tailed modeling and its connections to long range dependence. Heavy tailed modeling frequently implies infinite variances and thus departs from Gaussian methods. Broad themes of the research program include parameter estimation and prediction in heavy tailed models, model selection and confirmation, and the interplay between long range dependence and heavy tails. Special attention is given to application areas which include the financial and commodities markets and teletraffic networks such as the World Wide Web. Both probabilistic modeling and statistical issues are emphasized. Statistical issues include coping with changes of methods implied by non-standard data features such as long range dependence, lack of existence of moments and correlations, and dependencies which cannot be captured by linear structures. Probabilistic models will be formulated and studied in an attempt to qualitatively explain observed features of the data. The increasing instrumentation of both financial markets and broadband data networks makes possible the collection of huge quantities of data. Examination of some of the data reveals features that classical statistics and probability models are not used to dealing with and hence, this project has a dual purpose: (a) To develop statistical tools which use the data to more reliably fit models and make predictions; (b) To build probability models which provide qualitative insights into the nature of the system under investigation. For example, modern broadband networks exhibit characteristics much different from what is predicted by classical models. A question which may be answered by this research is, "when is it economically advisable to add service capacity to the network?".