A Gini-Based Methodology for Identifying and Analyzing Time Series with Non-Normal Innovations

The objective of this paper is to suggest a visual method for identifying departures from normality of the innovations in times series models. The method is based on replacing the variance by the Gini as the measure of variability. The Gini methodology is a rank-based methodology, which takes into account both the variate values and the ranks. It relies only on first order moment assumptions hence it is valid for a wider range of distributions. The key idea lies in the fact that there are two Gini-autocorrelation functions for each pair of variables, which are not necessarily equal. The difference between them, when it exists, can be informative and may assist to identify models with underlying heavy tailed and non-normal innovations. We suggest using Gini-correlograms, a simple graphical tool, to check the symmetry assumption which is natural in the existing methodology. We illustrate the suggested methodology using simulations