In the second part of a two-part article, David Aronson, President of Hood River Research, examines the modelling techniques used in arriving at a valuable predictor set for boosting ‘raw’ trading model performance.

The Role of Advanced Models in Performance Boosting

The development of a boosting model is a two-stage process. The first is discovering which, if any, of the large list of candidate indicators proposed for consideration are helpful in predicting signal returns. The second is establishing the shape of the surface that best describes the relationship between the selected candidate indicators and signal returns. One widely used modelling technique is multiple linear regression, which assumes that the shape of the surface is linear (flat with no hills and valleys). Only the slope of the surface with respect to each axis (i.e. the weight of each indicator) is left open to discovery. However, modern data modelling techniques have allowed the constraining assumption of a flat surface to be eliminated. This allows the modelling procedure to discover the most appropriate shape for the model’s hyper-surface1.

Advanced modelling vs. linear regression

As powerful as multiple linear regression is, relative to the intuitive judgment of human experts, greater predictive power can be attained with more advanced modelling methods that are not constrained by the simplifying assumption of linearity. This creates the opportunity for more accurate predictions of signal outcomes. Advanced methods such as kernel regression can detect complex non-linear relationships. Figures 1 to 5 illustrate how more sophisticated non- linear modelling differs from traditional linear regression. For simplicity, the illustrations depict a single indicator (Xi) on the horizontal axis and the return earned by the signal on the vertical axis. Figure 1 shows the true functional relationship between signal returns and Xi, which is unknown in the sense that the true shape of the function sought in any predictive modelling problem is by definition unknown and remains to be inferred from an observed sample of data. Note that the relationship is not linear. ...

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