Increasing robustness - averaging over more portfolios:

For completeness we mention here that we have evaluated the models in the multivariate context as an average over 2 portfolios with opposing position vectors - equally weighted and long on the US Dollar against all series k and equally weighted and short on the US Dollar against all series k. For a more complete analysis it is viable to extend the methodology by averaging over a larger set of position vectors (such as for example on a sphere of dimension k with some appropriate radius), always ensuring that the symmetrically opposed portfolio is also included.