QUESTION:
I understand regression, but I don't understand what a Transfer Function is. Can you explain the difference?ANSWER:
A regression model, like any other model, is only as good as its form. What I mean by form is; a. Correct lag/lead specification for the user specified x's b. Correct specification for the error process. Economists refer to model specification bias as a major problem, which unfortunately can never be remedied by estimation. The fix for MSB is a redefined model. Let us first examine (a). The exact form of the relationship between the series must be specified either initially or via diagnostic checking ultimately. Consider the case where Y(t) = W X(t-3) + N(t). If you incorrectly specify Y(t) = W X(t) + N(t) then you conclude that there is no relationship. The problem is that the relationship is not-contemporary but a lagged one of order 3. Temporal relationships like leads are prevalent in the consumer products industry where sales arise in advance of the holiday and often are reduced the week of the holiday. The correct lag structure Y(t) = W(B) X(t) + N(t) might require a polynomial lag, not necessarily describable by a smooth curve. Sometimes the relationship is optimally modeled by the ratio of two poynomials W(B) and D(B).
W(B)
T(B)
Y(t)
= -------- X(t) + ---------- A(t)
D(B)
P(B)