Least Squares Estimation and Order Selection for Heavy-Tailed ARMA Time Series with GARCH Innovations

• Activity Number: 308
• Type: Contributed
• Date/Time: Tuesday, August 2, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): Huanhuan Wang*+ and Beth Andrews
• Companies: Northwestern University and Northwestern University
• Keywords: Autoregressive-moving average ; GARCH ; least-squares estimation ; order selection

Abstract

Since least-squares is a standard preliminary estimation technique, we consider properties of least-squares estimators for autoregressive-moving average (ARMA) time series model parameters when the ARMA process is heavy-tailed with GARCH innovations and tail index in the interval (2,4). These ARMA-GARCH series have infinite fourth but finite second moments, properties exhibited by many observed time series, particularly in finance. In this case, the least-squares estimators of the ARMA model coefficients are consistent and converge in distribution to a function of non-Gaussian stable random variables, with rate of convergence slower than n^{1/2}. Using the asymptotic distribution for the least-squares estimators, we identify information criterion statistics which can be used for consistent estimation of ARMA model order. We examine finite sample behavior of the ARMA estimators and order selection statistics via simulation, and the techniques are used to fit an ARMA-GARCH model to heavy-tailed financial time series data.