Least Absolute Deviation Estimation for General Autoregressive Moving Average Time Series Models

• Activity Number: 584
• Type: Contributed
• Date/Time: Wednesday, August 3, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Rongning Wu*+ and Richard A. Davis
• Companies: The City University of New York and Columbia University
• Keywords: autoregressive moving average model ; least absolute deviation estimation ; noncausality ; noninvertibility

Abstract

In this paper, we study least absolute deviation (LAD) estimation for general autoregressive moving average (ARMA) time series models that may be noncausal, noninvertible or both when the underlying noise is non-Gaussian. For stationary ARMA models with Gaussian noise, causality and invertibility are assumed in order for the parameterization to be identifiable. The assumptions, however, are not required for models with non-Gaussian noise, and hence are removed in our study. We deconstruct a stationary ARMA model into its causal, purely noncausal, invertible and purely noninvertible components, and formulate the proper LAD objective function. Following the approach taken by Davis and Dunsmuir [Least absolute deviation estimation for regression with ARMA errors, Journal of Theoretical Probability 10 (1997) 481-497], we derive a functional limit theorem for random processes based on the LAD objective function, and establish the consistency and asymptotic normality of the LAD estimator. The performance of the estimator is evaluated via simulation and compared with the asymptotic theory. Application to a financial time series consisting of volumes of traded stocks is also provided.