Some results in periodic autoregression

Abstract

SUMMARY Several properties of a periodic autoregressive process {x8} are examined by considering a related stationary multivariate autoregressive process. The properties of interest include: the representation of x8 as an infinite linear combination of independent, periodically distributed random variables, constraints on the parameters which permit such a representation, the covariance and spectral properties of {x8}, and the asymptotic behaviour of cumulative sums of {x8} and of functions of these sums.