Wavelet Neural Networks: With Applications in Financial Engineering, Chaos, and Classification

5 Variable Selection: Determining the Explanatory Variables

As mentioned in earlier chapters, the model identification procedure is divided into two parts: model selection and variable selection. In this chapter we focus on the second part of the model identification procedure, variable selection.

The use of absolutely necessary explanatory variables is known as the principle of parsimony, or Occam's razor. In real problems it is important for various reasons to determine correctly the independent variables. In most financial problems there is little theoretical guidance and information about the relationship of any explanatory variable with the dependent variable. As a result, unnecessary independent variables are included in the model, reducing its predictive power. The use of irrelevant variables is among the most common sources of specification error. Also, correctly specified models are easier to understand and to interpret. The underlying relationship is explained by only a few key variables, while all minor and random influences are attributed to the error term. Finally, including a large number of independent variables relative to sample size (an overdetermined model) runs the risk of a spurious fit.

To select the statistical significant and relevant variables from a group of possible explanatory variables, an approach involving the significance of statistical tests of hypotheses is followed. To do so, the relative contributions of the explanatory variables in explaining ...