A Measure of Early Warning of Exchange-Rate Crises Based on the Hurst Coefficient and the Αlpha-Stable Parameter

The Hurst coefficient and the alpha-stable parameter are useful indicators in the analysis of time series to detect normality and absence of self-similarity. In particular, when these two features met simultaneously, it is said that the series is driven by white noise. This paper is aimed at developing an index to measure the degree to which a time series departs from white noise. The proposed index is built by using the principal component analysis of the Mahalanobis distances between the Hurst coefficient and the alpha-stable parameter from theoretical values of normality and absence of self-similarity. A zero value of the index corresponds to a pure white noise process, while a 100 value correspond to the maximum distance between the actual series and the theoretical white noise. The proposed index is applied to examine the exchange rate of the Mexican peso against the USA dollar. When examining the exchange rate, one distinctive finding of the Index is that it can be used as an early warning indicator of crises, as it is shown for the Mexican case.