Mathematical Sciences: Long Memory and Infinite Variance

数学科学：长记忆和无限方差

• 批准号: 9404093
• 负责人: Murad Taqqu
• 金额: --
• 依托单位: Trustees of Boston University
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-01 至 1999-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9404093&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Long; Memory; Infinite

9404093 Taqqu This research concerns the investigation of the time series with long memory and/or infinite variance. Long memory, in the finite variance case, occurs when the covariances tend to zero like a power and the spectral density diverges at the origin. This behavior has been observed in many real-life phenomena. Sometimes long memory occurs jointly with infinite variance, for example when the underlying process is stable but not Gaussian. In this case it is the tail of the distribution that decays like a power function. The research will focus on the probabilistic and statistical properties of time series with long memory and/or infinite variance. Most of the available statistical techniques assume that the data to be analyzed are not very dependent. However, in a number of areas such as economics and geophysics, the data can display long range dependence and can also sometimes fluctuate significantly from their mean value. The goal of this research is to develop new techniques for modeling and analyzing this type of data.

9404093塔库这项研究是关于具有长记忆和/或无限方差的时间序列的研究。在有限方差的情况下，当协方差像幂一样趋于零并且谱密度在原点发散时，发生长记忆。这种行为在许多现实生活现象中都能观察到。有时长记忆伴随着无限的变化而发生，例如，当潜在的过程是稳定的但不是高斯的时候。在这种情况下，分布的尾部像幂函数一样衰减。研究的重点是具有长记忆和/或无限方差的时间序列的概率和统计性质。大多数可用的统计技术都假定要分析的数据不是非常相关的。然而，在一些领域，如经济学和地球物理学，数据可能表现出长期相关性，有时也可能与其平均值显著波动。这项研究的目标是开发新的技术来建模和分析这种类型的数据。