The choice of restricting our time series to east of 100° W highlights one of the first decisions in time series modeling - the spatial extent over which yields and weather are averaged. This scale can range from individual fields (if the data are available) to entire regions. As scales become bigger, datasets are often more reliable and available. However, aggregating areas too large will result in combining fields that actually behave quite differently. Consider, for example, two adjacent areas, one of which prefers cooler climates and the other of which prefers warmer climates. If these two are combined, then the average yields could show no effect of climate variations even though there is a true response in each region. If the only goal is to understand yield responses at the broader scale, then one might be satisfied with this result. But, in general, we prefer when possible to work with regions that are relatively homogeneous in nature. Separating irrigated from rainfed crops is almost always a good idea, given the very different nature of response to rainfall.
The scale issue also extends to the temporal dimension. Just as maize in California may be functionally a very different crop than maize in Georgia, maize in 1950 was potentially very different in its climate response than maize in 2000. For example, Zhang et al. (2008) demonstrate that the correlation between rice yields and temperature in China switched from being negative before 1980 to positive after 1980. The explanation in this instance was that irrigation was much more widespread after 1980, allowing crops to take advantage of the drier, sunnier conditions that led to water stress for rainfed crops. The time period for time series analysis should therefore be restricted to periods over which management was reasonably constant, particularly management factors such as irrigation that can strongly influence climate responses. One approach to ensure a stationary relationship between climate and yields is to perform the analysis for the first and second half of the record, and then compare the results.
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