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

布鲁斯 这个小企业创新研究第一阶段项目将开发用于治疗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，集成，移动平均）过程，这是一类扩展标准自回归，集成，移动平均过程以包括长记忆组件的过程。 第一阶段的研究将在以下领域扩展现有的FARIMA建模方法：（一）模型选择;（二）稳健的参数估计;（三）对缺失值的时间序列的估计;以及（四）使用小波方差评估FARIMA建模背后的假设。 还将编写一本从业人员案例手册，说明和指导FARIMA模型在科学和工程中的使用。 在物理学、海洋学、天文学、电子工程、经济学、生理学和其他学科中经常遇到的时间序列表现出长记忆过程的特性。 这个过程的本质是，随机变量之间的相关性不会随着变量之间时间间隔的增加而迅速接近零。 使用具有长记忆时间序列的标准时间序列方法可能导致不正确的统计分析;例如，平均值的置信区间在数量级上可能过于乐观。 长记忆时间序列是科学的基础，处理这些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，该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-Plus模块销售，并许可用于其他商业应用。 根据从业者的案例手册，教学材料将作为书籍和超媒体销售。 ***

*** 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. ***