###
QUENOUILLE-TYPE THEOREM ON AUTOCORRELATIONS

###
SIMON KU AND EUGENE
SENETA

*School of Mathematics and Statistics, The University of
Sydney,
N.S.W. 2006, Australia*
(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.

**Source**
( TeX ,
DVI ,
PS )