Similar to the alpha risk, a large prediction error (MPE), such as that for the X-11 model, can lead to anomalies resulting in very low or high beta risks regardless of the width of the confidence interval.
TABLE 4 Relationships Among Confidence Interval Width, Risk, and Testing Approach (a) Confidence Interval Width Risk Level Alpha Risk ([absolute value of E]=0): Positive Approach Wider Lower (Control Point) Negative Approach Wider Higher Beta Risk ([absolute value of E]=M): Positive Approach Wider Higher Negative Approach Wider Lower (Control Point) (a) Assuming the predicted values (P) and actual values (A) are reasonably close.
As a result, the alpha risk for the positive approach is expected to be the same for all the models because a common rejection area ([alpha] =.33) is applied to each model.
For the positive approach, it is apparent from table 6 that the ARIMA and Martingale models yield the lowest alpha risk. The alpha risk for both of these models is closer to the specified control point ([absolute value of E]=0) risk of [alpha] =.33.
In term of alpha risk, the structural and stepwise models yield the lowest alpha risk for both time periods for the negative approach.
This would cause a large alpha risk and a small beta risk.
