Rank-Based Estimation for Infinite Variance Autoregressive Processes with Regularly Varying Tail Probabilities

• Activity Number: 441
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 2:00 PM to 3:50 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): Jiening Chen*+ and Beth Andrews
• Companies: Northwestern University and Northwestern University
• Keywords: Time series ; autoregressive models ; heavy-tailedness ; Stable distribution ; rank estimation ; robustness

Abstract

In this paper, we use rank-based methods to study estimation for univariate autore-gressive processes with regularly varying tail probabilities. Our rank-based estimatoris obtained by minimizing a criterion function constructed from both residuals and their ranks. Our research shows the rank technique is robust and e?cient compared to existing estimation methods. Under general conditions, when the tail index for the autoregressive process is in the interval (0,2), we show rank estimators are consistent and converge in distribution to the minimizer of a random function, with a rate of convergence faster than sqrt(n) where n represents sample size. We also examine the performance of the rank estimators for ?nite samples via simulation, and show rank estimators have smaller mean squared error than existing estimators.