ON THE ASYMPTOTIC DISTRIBUTION OF THE GENERALIZED PARTIAL AUTOCORRELATION FUNCTION IN AUTOREGRESSIVE MOVING‐AVERAGE PROCESSES

Byoung Seon Choi

Journal of Time Series Analysis, 1991, vol. 12, issue 3, 193-205

Abstract: Abstract. It has been conjectured and illustrated that the estimate of the generalized partial autocorrelation function (GPAC), which has been used for the identification of autoregressive moving‐average (ARMA) models, has a thick‐tailed asymptotic distribution. The purpose of this paper is to investigate the asymptotic behaviour of the GPAC in detail. It will be shown that the GPAC can be represented as a ratio of two functions, known as the θ function and the Λ function, each of which itself has a useful pattern for ARMA model identification. We shall show the consistencies of the extended Yule‐Walker estimates of the three functions and present their asymptotic distributions.

Date: 1991
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