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Title: Spectral Procedures Enhance the Analysis of Three Agricultural Time Series

item Meek, David
item Prueger, John
item Tomer, Mark
item Malone, Robert - Rob

Submitted to: Applied Statistics In Agriculture Conference Proceedings
Publication Type: Abstract Only
Publication Acceptance Date: 5/30/2007
Publication Date: 6/1/2007
Citation: Meek, D.W., Prueger, J.H., Tomer, M.D., Malone, R.W. 2007. Spectral Procedures Enhance the Analysis of Three Agricultural Time Series [abstract]. In: Applied Statistics In Agriculture Conference Proceedings, April 30-May 1, 2007, Manhattan, KS. p. 17.

Interpretive Summary:

Technical Abstract: Many agricultural and environmental variables are influenced by cyclic processes that occur naturally. Consequently their time series often have cyclic behavior. This study developed times series models for three different phenomenon: (1) a 60 year-long state average crop yield record, (2) a four year-long daily stream flow record, and (3) a half-hour long wind speed record sampled at 10 hertz. Trend tests, simple high pass filtering, and spectral analysis on original and detrended and residual data series were used to guide model development. The stream flow data were aggregated to weekly averages. The wind speed data were aggregated to 10 second averages. Then, as a means to provide insight to the researchers, nonlinear regression procedures were used to develop models in the time domain. The models considered may have a large scale trend, low to high frequency cycles, and, if need be, an autoregressive (AR) error structure. Selected models for all three sets included a trend component. The model for yield also included two high frequency cycles of 2.5 and 3.8 years. The model for stream flow included an annual, semiannual, and almost quarterly cycles with an AR1 error structure. The model for wind speed had an intermediate cycle (13 min) and three smaller scale (<10 min) cycles with an AR1 error structure. The use of time series methods instead of the inverse transform on selected frequencies allows for simultaneous estimation of all components. Moreover it opens the door to the use of a much broader class functions to model the trend, to the use of other kinds of periodic functions to model the cycles, and to the incorporation of structure in the error term.