(Received May 22, 1995; revised February 1, 1996)
Abstract. The central result is a limit theorem for not necessarily stationary processes resembling AR(p). Assumption of a vector limit distribution for standardized sample autocorrelations leads to the convergence of a vector limit distribution for ordinary sample partial autocorrelations, and to a clear relationship between the two limit distributions. The motivation is the study of the case p = 1 by Mills and Seneta (1989, Stochastic Process Appl., 33, 151-161). The central result is used to explain the nature of the relationship between the two results of Quenouille in the classical stationary AR(p) setting.
Key words and phrases: Limit theorem, sample autocorrelations, sample partial autocorrelations, Quenouille's test.
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