SPECTRAL PROCEDURES ENHANCE THE ANALYSIS OF THREE AGRICULTURAL TIME SERIES

Abstract

Many agricultural and environmental variables are influenced by cyclic processes that occur naturally. Consequently their time series often have cyclic behavior. This study develops time series models for three different phenomena: (1) a 60 year-long state annual average crop yield record, (2) a four year-long daily stream flow record with values aggregated to weekly averages, and (3) a half-hour long wind speed record sampled at 10 hertz with values aggregated to 0.5 min averages. Trend tests, simple high pass filtering, and spectral analysis on original and detrended and residual data series are used to guide model development. Next, as a means to provide insight for researchers, nonlinear regression procedures are 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 has a linear trend in time and includes two high frequency cycles of 2.3 and 2.5 years. The model for stream flow has a complicated trend consisting of splined polynomials in the square root of time. Cycles include an annual and approximately 8, 6, and 3 month periods. Also an AR1 error structure is added. Results suggest the wind speed can be modeled as a superposition of damped and undamped oscillations. A zero order fractional Bessel function models the trend, here a damped oscillation with a period of 10.5 min. Smaller scale regular cycles of 6.6, 3.3 and 2.2 min are added along 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 of 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. This approach may provide useful insight and a methodological approach for several ongoing and some future studies at the National Soil Tilth Laboratory.