Fitting Linear Time Series Models via the Gini Autocovariance Function

• Activity Number: 235
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Marcel Carcea*+ and Robert Serfling
• Companies: and University of Texas at Dallas
• Keywords: Linear time series ; autocovariance ; heavy tails ; outliers ; model fitting

Abstract

Many time series settings in economics, finance, and actuarial science involve heavy tailed distributions and data. A typical case is that first moments are finite but not second moments. Without second-order assumptions, the usual autocovariance function is unavailable, although the sample version still can be used. However, the "Gini autocovariance function" is well-defined under just first-order moment assumptions. Here we focus on the fitting of linear time series models, which play a central role, and we allow heavy tailed innovations or contaminants. Estimators of the model parameters based on a 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, and it is seen that the "Gini" approach competes very well with standard methods and is superior in some cases, thus providing a tool usefully augmenting existing methods.