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

*** 9661424 Bruce这个小企业创新研究第一阶段项目将开发时间序列方法来处理长记忆时间序列。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，移动平均过程的过程，以包括长记忆组件。第一阶段的研究将在以下方面扩展现有的FARIMA建模方法：(I)模型选择；（ii）稳健参数估计；（iii）缺失值时间序列的估计；（iv）利用小波方差评估FARIMA建模背后的假设。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应用。在地球物理学、海洋学、天文学、电气工程、经济学、生理学等学科中常见的时间序列表现出长记忆过程的特性。这一过程的实质是随机变量之间的相关性不会随着变量间时间间隔的增加而迅速趋近于零。使用标准时间序列方法与长记忆时间序列可能导致不正确的统计分析；例如，均值的置信区间可能过于乐观。长记忆时间序列是科学的基础，一个完整的处理这些序列的统计方法将对科学进步做出重大贡献。如果成功，这项研究将产生一个软件工具包，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，并授权给其他商业应用。根据实践者的案例手册，教学材料将以书籍和超媒体的形式销售。＊＊＊

*** 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. ***