A Gini Autocovariance Function for Time Series Modeling

www.utdallas.edu/∼serfling. An important conceptual and methodological tool in time series modeling, the autocovariance function (ACF), presupposes finite variances and thus excludes heavy tailed distributions and data. This paper introduces an alternative that captures some key features of the ACF assuming just first order moments, the “Gini autocovariance function ” (GACF). It adds a useful new tool to the various existing approaches for dealing with heavy tailed time series data. For example, accommodating semiparametric modeling of linear time series, equations based on the GACF are derived for fitting autoregressive, moving average, and ARMA models. Also, accommodating parametric modeling, the GACF for a nonlinear heavy-tailed autoregressive (Pareto) model is developed and sheds new light not available through the usual ACF even when defined. A sample GACF is formulated that is convenient to evaluate