Anon

Model Estimation 273

In order to decide what approximation is the best, we could use AIC or BIC
criteria as discussed in Appendix E.
In the preceding illustration we used two different functional forms, a
straight line, which is a polynomial of degree one, and a polynomial of degree
two. The LS method can be adapted to any set of data points and to different
functional forms (straight lines, polynomial functions, and so on). The choice
of the functional form depends on both theoretical and statistical consider-
ations. Theoretical considerations might suggest a specific functional form
to approximate the data. For example, suppose our objective is to model a
series of market capitalization data of some firm. Theoretical considerations
on firm growth will probably suggest that we try an exponential function.

ordinary least Squares Method

Thus far we have illustrated LS methods as a technique to find an optimal
approximation to data and we have not made any statistical assumptions.
However, the LS method also applies to statistical models, in particular
to regressions, as we have seen in Chapter 3. As explained above, the LS

0 2 4 6 8 10 12

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

x

y

FigUre 13.4 Scatterplot of Sample Data and Plot of the Best Fitting Polynomial of
Second Degree