α)+α∕2] x mth largest of the resulting m simulated price realization values. The former process is programmed
in Gauss 386i with m=100,000 and repeated for t=0,...49 under the normal and non-normal corn and soybean
price models. The resulting boundaries are joined to obtain (1-α)% confidence bands for the 50 individual
price predictions and for the 50 individual price realizations observed from 1951 to 2000.
The 95% confidence bands for the soybean price predictions, i.e. for the expected soybean prices, and
for the actual price occurrences under the normal and non-normal regression models are presented in Figures 1
and 2. The predictions, and the corresponding confidence bands, do not follow the typical curvilinear shape of
a second-degree polynomial in this case because they are autocorrelated predictions (Judge, et al., p. 316). The
95% bands for the 50 soybean price predictions under the normal model show an average width of $0.714/bu
versus $0.557/bu under the non-normal model, i.e. they are 28% wider, on average. The 95% confidence
bands for the 50 corn price predictions are 35% wider under the normal model than under the non-normal
model, on average. An evaluation of the 80% to 95% confidence bands for both price series finds similar (28%
to 35%) average percentage width differences at all 16 certainty levels.
In short, the non-normal models produce more precise predictions for the corn and soybean prices to
be expected at any given year. Realistic confidence bands for the actual price occurrences, however, are as
important in applied research. Figures 1 and 2 also show the 95% confidence bands for the soybean price
occurrences under the normal and non-normal models. In the normal case (Figure 1), the bands are wider than
those constructed for the predictions, but they are still symmetric about the price predictions. This is due to the
addition of the normally distributed error term. Note that two of the price realizations exceed the upper bound
while none is located even close to the lower bound, versus the theoretically required number of 1.25.
Examination of the 80 to 95% confidence bands reveals that, from 83% to 95%, no observations are
left below the lower bounds, and only two are beneath the 80% band versus the theoretically required number
of five (Table 4). When all of the 16 confidence bands are considered, only five out of a theoretically required
total of 50 observations are found below the lower bounds, while 58 are above the upper bounds (Table 4).
The assumption of error term normality, which causes these confidence bands to be symmetric, appears
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