Entropic Efficiency of Currency Markets

Financial markets are generally categorised as either efficient or inefficient with respect to each of three nested information sets: weak form (historical prices), semi-strong form (publicly available information) and strong form (all information). It would be more appropriate to treat these markets as being neither perfectly efficient nor perfectly inefficient, but as existing in varying degrees of efficiency.

In this paper we modify and apply the ‘conditional fuzzy entropy’ statistic (FuzzyEn), to obtain a ‘normalised fuzzy entropy’ statistic (N-FuzzyEn), and directly measure the degree of efficiency. For a given grid and template sizes (say, r=0.2, m=2) one can compute the conditional fuzzy entropy for any price timeseries. Using the same grid and template sizes and the fitted empirical probability density, one can also determine the corresponding unconditional fuzzy entropy. Subsequently normalising the conditional fuzzy entropy (FuzzyEn) statistic by division using the corresponding unconditional entropy statistic begets a normalised measure i.e. the N-FuzzyEn statistic, thus achieving distributional (and consequently scale) invariance within the range [0,1].

To test the effectiveness of the N-FuzzyEn statistic, we use it to measure and rank 21 currency markets in terms of their degree of efficiency. The results corroborate the commonly observed dissociation between ‘de jure’ and ‘de facto’ currency regimes.