Premium
ON THE ASYMPTOTIC DISTRIBUTION OF THE GENERALIZED PARTIAL AUTOCORRELATION FUNCTION IN AUTOREGRESSIVE MOVING‐AVERAGE PROCESSES
Author(s) -
Choi Byoung Seon
Publication year - 1991
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.1991.tb00077.x
Subject(s) - mathematics , partial autocorrelation function , autocorrelation , autoregressive–moving average model , autoregressive model , moving average model , moving average , function (biology) , asymptotic analysis , distribution (mathematics) , asymptotic distribution , autoregressive integrated moving average , statistics , mathematical analysis , time series , estimator , evolutionary biology , biology
. 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.