The mahalanobis distance between the hurst coefficient and the Alpha-Stable parameter: An early warning indicator of crises

Abstract

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 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. The proposed index is applied to examine the Mexican Peso exchange rate against the US Dollar. The distinctive characteristic of the index is that it can be used as an early warning indicator of crises, as it is shown for the Mexican case.