100 The Basics of financial economeTrics
series typically exhibit structures that are more complex than those pro-
vided by ARMA models, these models are a starting point and often serve as
a benchmark to compare more complex approaches. There are two compo-
nents to an ARMA model: (1) autoregressive process and (2) moving aver-
age process. We discuss these in Chapter 9.
Key Points
■ (^) The structure or interaction of the independent variables is an impor-
tant issue in a multiple linear regression model and is referred to as the
multicollinearity problem. Investigation for the presence of multicol-
linearity involves the correlation between the independent variables and
the dependent variable.
■ (^) Tests for the presence of multicollinearity must be performed after the
model’s significance has been determined and all significant independent
variables to be used in the final regression have been determined.
■ (^) The process of building a multiple linear regression model involves
identifying the independent variables that best explain the variation in
the dependent variable.
■ (^) In the initial development of a model, how many and which indepen-
dent variables to include in the model are unknown. Increasing the
number of independent variables does not always improve regressions.
■ (^) Pyrrho’s lemma states that by adding one special independent variable
to a linear regression model, it is possible to arbitrarily change the sign
and magnitude of the regression coefficients as well as to obtain an
arbitrary goodness-of-fit.
■ (^) Without a proper design and testing methodology, the adding of inde-
pendent variables to a regression model runs the risk of obtaining spuri-
ous results.
■ (^) Stepwise regression analysis is a statistical tool employed for determin-
ing the suitable independent variables to be included in a final regression
model. The three stepwise regression methodologies are the stepwise
inclusion method, the stepwise exclusion method, and the standard
stepwise regression method.
■ (^) The process of building a model also calls for testing the assumptions of
the multiple linear regression model (i.e., performing diagnosis checks).
■ (^) The diagnosis checks analyze whether the linear relationship between
the dependent and independent variables is justifiable from a statistical
perspective.
■ (^) These tests also involve testing for the several assumptions that are made
when using the general multiple linear regression model: (1) independence