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

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*** 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. ***