The asymptotic distribution of the constant behavior of the generalized partial autocorrelation function of an ARMA process

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.