Fitting Heavy-Tailed Nonlinear (Pareto) Autoregressive Time-Series Models

• Activity Number: 356
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 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 ; nonlinear ; heavy tails ; Pareto ; Gini Autocovariance

Abstract

Heavy tailed distributions and data are becoming mainstream in time series settings in economics, finance, and actuarial science, for example. For such purposes, classical second order moment assumptions need to be relaxed. Also, nonlinear structure is becoming increasingly of interest. Here we present contributions toward fitting a nonlinear heavy tailed autoregressive time series model of Pareto type, ARP(1). We focus on the role of a recently developed "Gini autocovariance function" that is well-defined under just first-order moment assumptions, and we discuss both model-based and empirical sample versions. Further, a new simple estimator of the tail index of ARP(1) is discussed. Finally, a diagnostic is presented for deciding whether to fit a standard linear autoregressive model AR(1) or an ARP(1) model to any given time series data set.