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Biometrika 1976 63(3):681-683; doi:10.1093/biomet/63.3.681
© 1976 by Biometrika Trust
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Miscellanea

On two convex autocorrelation regions for moving average processes

O. D. ANDERSON

Civil Service College London

The set of autocorrelations, 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 , 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.

Key Words: Borderline noninvertibility • Fejér-Riesz theorem • General autoregressive-moving average process • Invertibility • Rayleigh mapping • Seasonal process • Spectral density function


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