M-Estimation for General ARMA Processes with Infinite Variance

• 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): Rongning Wu*+
• Companies: Baruch College
• Keywords: ARMA process ; bootstrap ; infinite variance ; M-estimation ; non-causality ; non-invertibility

Abstract

General autoregressive moving average (ARMA) models extend the traditional ARMA models by removing the assumptions of causality and invertibility. The assumptions are not required under a non-Gaussian setting for the identifiability of the model parameters in contrast to the Gaussian setting. We study M-estimation for general ARMA processes with infinite variance, where the distribution of innovations is in the domain of attraction of a non-Gaussian stable law. Following the approach taken by Davis et al. (1992) and Davis (1996), we derive a functional limit theorem for random processes based on the objective function, and establish asymptotic properties of the M-estimator. We also consider bootstrapping the M-estimator and extend the results of Davis & Wu (1997) to the present setting so that statistical inferences are readily implemented. Simulation studies are conducted to evaluate the finite sample performance of the M-estimation and bootstrap procedures. An empirical example of financial time series is also provided.