A Gini Autocovariance Function for Time Series Modelling

In stationary time series modelling, the autocovariance function (ACV) through its associated autocorrelation function provides an appealing description of the dependence structure but presupposes finite second moments. Here, we provide an alternative, the Gini ACV, which captures some key features of the usual ACV while requiring only first moments. For fitting autoregressive, moving-average and autoregressive-moving-average models under just first-order assumptions, we derive equations based on the Gini ACV instead of the usual ACV. As another application, we treat a nonlinear autoregressive (Pareto) model allowing heavy tails and obtain via the Gini ACV an explicit correlational analysis in terms of model parameters, whereas the usual ACV even when defined is not available in explicit form. Finally, we formulate a sample Gini ACV that is straightforward to evaluate.