residuals rejects the null hypothesis of error term normality at the 1% level, supporting this conclusion.
The confidence bands for the basis predictions and occurrences are generated using the same numerical
procedures described in the case of the corn and soybean price models. As before, few key summary statistics
about the bands are more revealing than their graphical presentation. As a result of the larger standard errors, the
80 to 99% confidence bands for the predictions from the normal model are, on average, 63% wider than those
from the non-normal model, i.e. the later produces substantially more precise predictions of the West Texas
cotton basis. As in the corn and soybean price models, the NNHAR(4) confidence bands for the actual basis
occurrences are more “efficient” and theoretically consistent than the bands from the normal model (Table 6).
They are more efficient in the sense that they are substantially narrower (7.306 vs. 9.643 basis points), on
average, and at all 20 α levels evaluated, although, as before, they approach the width of the normal bands the
lowest α of 0.01. At the same time, the 80 to 99% non-normal confidence bands are more theoretically consistent
since the numbers of observations found below and above their lower and upper bounds are much closer to the
theoretically expected numbers (Table 6). The more reliable non-normal confidence bands of the West Texas
cotton basis are clearly useful for applied research and decision making about futures contracting.
Another interesting and original byproduct of the NNHAR(4) model is the finding that, in addition to
affecting the mean and variance, policy and seasonal variables can also shift the skewness and kurtosis of the
error term distribution and, thus, of the conditional distribution of an economic time series. The estimated
conditional distributions of the West Texas cotton basis for the two seasons under the three policy periods in
the analysis are presented in Figures 4 and 5, assuming the average values for all other explanatory variables
during the corresponding season and policy period.
Note the substantial kurtosis and right skewness of the distributions during the March to July planting
season. In the current, post-1985 Farm Bill period, for example, the distribution shows a mean of -2.62 and a
standard deviation of 2.83. It implies a 0.3% (5%) probability of a basis realization that is less (more) than
one standard deviation from the mean, versus the 16% expected under a normal distribution. The conditional
distributions of the West Texas cotton basis before and during the 1985 Farm Bill period had estimated means
20