A Gini Autocovariance Function for Time Series Modeling

fully acknowledged. A key conceptual and methodological tool in time series modeling is the auto-covariance function, which, however, presupposes finite variances and excludes heavy tailed distributions and data. To allow for the latter, which are increas-ingly of interest in modern statistics, this paper introduces a “Gini autocovari-ance function ” defined under merely first order moment assumptions. Playing roles similar to those of the usual autocovariance function, it provides a new fundamental tool for nonparametric description and modeling of time series. It is seen how to fit autoregressive, moving average, and ARMA time series models using Gini autocovariances. Also, the Gini autocovariance function for a nonlinear heavy-tailed (Pareto) autoregressive model is developed and sheds new light on this model. A straightforward sample Gini autocovariance function is formulated and its properties are discussed