Comment: Adaptive Forecasting
评论了Chatfield关于区间预测的建议，指出常规公式依赖强假设且易误导，强调覆盖概率比区间长度更重要，并以美国失业率预测为例说明机械使用公式的问题。
I am not surprised by how far behind our profession is in calculating interval forecasts. After all, interval forecast is a concept not well formulated nor well understood by statisticians. On the other hand, I am amazed by Chatfield's expectation and his recommendation. Will he be satisfied when Formulas (4.1) and (4.2) are routinely used in practice? Will he be satisfied when the forecast intervals are sufficiently wide to cover all the data points in out-of-sample forecasts? I agree totally that point forecasts fail to provide uncertainty assessment of the future, and some assessment on uncertainty must be given in prediction. Are interval forecasts the solution to uncertainty assessment, however? In particular, I am unhappy about advocating the routine use of Formulas (4.1) and (4.2) in providing interval forecasts. First of all, the formulas require many strong assumptions including that (a) the underlying model is the true model, (b) the innovational distribution is normal, and (c) the forecasts are unbiased. Since these assumptions are always violated in practice, what can a practitioner do? Second, the probability statement associated with an interval forecast tends to be misleading. The actual coverage probability is often different from the stated probability coefficient. Is there not a danger that we might provide a false impression on the accuracy in probability statement when we give a 95% prediction interval (PI) based on these formulas? Third, judging a PI by its length is misleading. For a reasonable PI, the coverage probability is more relevant. Considering the example of Section 7, I can see the value of increasing the upper bound from 8.73 to 11.14 for the 12-step-ahead PI. I would regard lowering the lower bound from 2.66 to .86 as a disservice, however. Does Chatfield believe the U.S. quarterly unemployment rate is ever lower than 2.0? In this particular instance, widening the PI by lowering the lower bound, resulting from the mechanical use of formulas (4.1) and (4.2), seems questionable. At least, it is in conflict with common sense.