Hopefully this isn't too off topic. I've just received test results and disagree with some explanations of a question. The TA and I can't seem to resolve our differences and I'm starting to think maybe he is right that my understanding is wrong. Would appreciate some additional, unbiased insight on this problem if anyone has any.
The library has built a triple exponential smoothing (Holt-Winters) model of the number of books borrowed each day, using a multiplicative weekly cycle of seasonality (i.e., =7).
i. Every year on July 4, the library shoots off fireworks in its parking lot, so nobody is allowed to borrow books that day. The model only has a weekly seasonality, not an annual one. Is the model likely to over-predict or under-predict books borrowed on July 4 (or neither)?
ii. Is the model likely to over-predict or under-predict books borrowed on July 5 (or neither)? [Assume the library is open and allows borrowing on July 5.]
I'll pause here so that you have time to come up with a solution without my biased answer, and the actual result.
I correctly answered i.) as Over-predict. The model will over-predict because the closing day is an outlier of zero, while the model smooths this response to fall in line with the other Fridays.
I incorrectly answered ii.) as Neither; the correct answer was Under-predict.
My reasoning here is that because of the weekly seasonality (L=7), all other Fridays that came before will factor into the calculation of this trend. The outlier Friday would thus hardly impact the predictions of the collective Fridays at all let alone the other Saturdays.
I think the only way in which we would get an under-prediction is if the seasonal factor was L=365, or annually. That way the July 4th date would constantly be brought very low, becoming a seasonal pattern, and also impact the July 5th date due to the smoothing happening on the July 4th date.
Appreciate any insight.
