Penalized Order Selection Procedure for AR Process

• Activity Number: 31
• Type: Contributed
• Date/Time: Sunday, August 1, 2010 : 2:00 PM to 3:50 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Xiaodong Lin*+
• Companies: Rutgers University
• Keywords: ARMA ; Autoregressive ; Penalized likelihood ; LASSO ; SCAD

Abstract

Traditional ARMA processes have fundamental difficulties in modeling non-linear and long-memory time series. Models such as ARFIMA have been proposed to address this issue. The estimations of such models rely on an AR ($\infty$) representation or approximation. The choice of a practical finite AR order becomes crucial and presents challenges to the conventional order selection procedures like AICC and BIC. In this paper we propose to regularize the AR process by penalized likelihood methods. This includes selecting a finite order $p$ for the AR ($\infty$) processes and the significant lags for the resulting AR (p) model. We have shown that our penalized estimators are consistent and enjoy an oracle property. We have demonstrated our theoretical results by comprehensive simulation studies and an analysis of the deposit rates of foreign currencies.