Statistics & Probability Letters 75 (2005) 113–118 The asymptotic distribution of the constant behavior of the generalized partial autocorrelation function of an ARMA process Seongbaek Yi Division of Mathematical Sciences, College of Natural Sciences, Pukyong National University, 599-1 Daeyon 3-Dong, Busan 608-737, Korea Received 25 February 2004; received in revised form 5 April 2005; accepted 21 May 2005 Available online 1 July 2005 Abstract The two-way array of the generalized partial autocorrelations (GPAC’s) of an autoregressive moving- average (ARMA) model shows a constant behavior and a zero behavior, which are useful for ARMA model identification. In this paper the asymptotic joint distribution of the GPAC estimators of the constant behavior is derived, which shows the corresponding asymptotic variance increases geometrically as the lag does. r 2005 Elsevier B.V. All rights reserved. Keywords: Autoregressive moving average; Generalized partial autocorrelation function; Identification; Time series analysis 1. Introduction Consider the autoregressive moving-average (ARMA) model of orders p and q, fðBÞy t ¼ yðBÞv t , (1) ARTICLE IN PRESS www.elsevier.com/locate/stapro 0167-7152/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.spl.2005.05.004 Tel.: +82 51 620 6328; fax: +82 51 611 6356. E-mail address: sbyi@pknu.ac.kr.