SBIR Phase I: Statistical Analysis and Software for Long Memory Processes

SBIR 第一阶段：长记忆过程的统计分析和软件

• 批准号: 9661424
• 负责人: Andrew Bruce
• 金额: $ 7.49万
• 依托单位: Insightful Corporation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-01-01 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9661424&HistoricalAwards=false
• 关键词: SBIR; Phase; Statistical; Analysis; Software

*** 9661424 Bruce This Small Business Innovation Research Phase I project will develop time series methodology for treating long memory time series. The methodology will use FARIMA (fractional autoregressive, integrated, moving average) processes, a class of processes that expands the standard autoregressive, integrated, moving average processes to include a long memory component. The phase I research will extend existing FARIMA modeling methodology in the following areas: (i) model selection; (ii) robust parameter estimation; (iii) estimation for time series with missing values; and (iv) assessment of assumptions behind FARIMA modeling by use of the wavelet variance. A practitioner's casebook illustrating and guiding the use of FARIMA models in science and engineering will also be developed. Time series commonly encountered in geophysics, oceanography, astronomy, electrical engineering, economics, physiology and other disciplines exhibit the properties of a long memory process. The essence of such a process is that correlation between random variables does not approach zero rapidly as the separation in time between the variables increases. Use of standard time series methodology with long memory time series can lead to incorrect statistical analysis; e.g., confidence intervals for the mean can be too optimistic by orders of magnitude. Long memory time series are fundamental to science, and a complete statistical methodology for handling these series will make a major contribution to scientific progress. If successful, the research will lead to a software toolkit offering a complete statistical methodology for FARIMA modeling. The toolkit will be marketed as an S-Plus module and licensed to other commercial applications. Based on the practitioner's casebook, instructional material will be marketed both as books and hypermedia. ***

*9661424布鲁斯这个小型企业创新研究第一阶段项目将开发处理长记忆时间序列的时间序列方法。该方法将使用FARIMA(分数自回归、整合、移动平均)过程，这是一类将标准自回归、整合、移动平均过程扩展为包括长记忆成分的过程。第一阶段的研究将在以下领域扩展现有的FARIMA建模方法：(1)模型选择；(2)稳健的参数估计；(3)有缺失值的时间序列的估计；以及(4)使用小波方差对FARIMA建模背后的假设进行评估。还将编写一本实践者案例手册，说明和指导FARIMA模型在科学和工程中的使用。时间序列在地球物理、海洋学、天文学、电气工程、经济学、生理学等学科中普遍存在，表现出长记忆过程的特性。这种过程的本质是，随着变量之间时间间隔的增加，随机变量之间的相关性不会迅速接近零。使用长记忆时间序列的标准时间序列方法可能会导致不正确的统计分析；例如，平均值的可信区间可能按数量级过于乐观。长记忆时间序列是科学的基础，处理长记忆时间序列的完整统计方法将对科学进步做出重大贡献。如果成功，这项研究将导致一个软件工具包，为FARIMA建模提供完整的统计方法。该工具包将作为S+模块销售，并授权给其他商业应用程序。根据从业者的案例手册，教学材料将以书籍和超媒体的形式销售。***