A Gini Autocovariance Function: Formulation, Properties, Estimation, and Applications

• Activity Number: 107
• Type: Invited
• Date/Time: Monday, August 1, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): Robert Serfling*+
• Companies: The University of Texas at Dallas
• Keywords: Time series ; Autocovariance ; Gini covariance ; Autoregressive models ; Moving average models ; ARMA models

Abstract

A new type of autocovariance function, the "Gini autocovariance function", is formulated under merely first order moment assumptions. It plays roles similar to those of the usual autocovariance function which, however, requires second order assumptions. Key properties of this new tool and suitable estimators are discussed. Systems of equations for the parameters of autoregressive (AR), moving average (MA), and ARMA models entirely in terms of the Gini autocovariance function are derived. For the AR case, these are linear, yielding convenient, easily interpreted, closed form expressions. Simulation results comparing the "Gini" estimators with least squares estimators for these models are discussed. Without second order assumptions, least squares estimators still perform best but lack population analogues, whereas the Gini sample versions are competitive and do possess population analogues as long as first order assumptions hold. Additional perspectives will be provided.