Robust Fitting of Heavy-Tailed Autoregressive Models Using Gini Autocovariance Functions

• Activity Number: 514
• Type: Contributed
• Date/Time: Wednesday, August 1, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Marcel Carcea*+ and Robert Serfling
• Companies: and The University of Texas at Dallas
• Keywords: Time Series ; Autoregressive ; Heavy Tails ; Outliers ; Gini AutoCovariance

Abstract

Many time series settings in economics, finance, and actuarial science involve heavy tailed distributions and data. The fitting of autoregressive models (AR) plays a central role. With heavy tailed innovations or contaminants, the usual second-order assumptions fail to hold. However, a "Gini autocovariance function" is well-defined under just first-order moment assumptions. Estimators for AR models based on a robustified sample Gini autocovariance function are linear, easily interpreted, and have closed form expressions. This talk presents results on their performance via simulation studies allowing a wide range of typical innovation and outlier scenarios. Comparisons are made with the Least Squares and Robust Least Squares approaches. The setting of nonlinear AR modeling is also treated. It is seen that the "Gini" approach competes very well with standard methods and provides a new reliable tool in time series modeling in heavy tailed settings.