Limited distribution of sample partial autocorrelations: A matrix approach

We develop a technique for derivation of the asymptotic joint distribution of the sample partial autocorrelations of a process, given the corresponding distribution of sample autocorrelations. No assumption of asymptotic normality is needed. The underlying process need not be stationary. The technique is demonstrated through a detailed study of ARMA (1,1)-like processes, but is applicable to other models. The results extend those of Mills and Seneta (1989) for the AR(1)-like case. The study is motivated by the known relationships and properties, especially is the classical AR(p) case, of population and sample partial autocorrelations.