Tail emphasis:

In model 5 we introduce the idea of tail emphasized fitting. As explained in section  - in this method, for every candidate parameter set the mean log-likelihood is computed only over the adverse half of the total number of contributing events in the in sample. To be precise, the log-likelihood contributions of all events in the in-sample are sorted and the mean is computed over the lowest half of the set. The consequent fitness landscape is considerably fractured since small changes in parameters can lead to the inclusion and exclusion of one or more events in the computation of the mean. Without the use of genetic algorithms [29] - for example by using only the BHHH algorithm - it would be quite impractical to find the optimal solution for such a fitness landscape.

It is important to note that adverse log-likelihood values are not necessarily contributed by the events of largest magnitude in the in-sample data. The tail referred to in the current context - is the tail in terms of bad predictions by a model - the tail of log-likelihood contributions. The tail emphasized optimization allows the model to find a parameter set which alleviates the problem with its worst predictions by compromising on its better predictions. It makes the model more homogeneous in the quality of its predictions and as a by product of this effect this model also shows better performance for large movements.