On two convex autocorrelation regions for moving average processes

Abstract

SUMMARY The set of autocorrelations { ρ 1 , … , ρ q } , ⁠ , for MA( q ), the general moving average process of order q , is considered, as a point in q -space. It is shown that the range of all such points is a convex region, which is a one-to-one map of the domain consisting of the sete of parameter points { θ 1 , … , θ q } ⁠ , corresponding to all invertible and borderline noninvertible MA.( q ) processes. It is also shown how an MA( q ) process can be decomposed into a set of independent first-order seasonal moving average processes, provided that its set of autocorrelations is contained in a certain hypercubic subrange of the convex region.