Unique decomposition of low-order time series

Eugene Seneta and Simon Ku

Communications in Statistics - Theory and Methods, 2016, vol. 45, issue 11, 3357-3366

Abstract: We give necessary and sufficient conditions on the parameters of processes ARMA(1, 1) and ARMA(2, 1) for representation of each as unique sums of independent simpler ARMA processes, including deduction from the sum process of the innovation variances of these summands. This work on inversion is motivated by examples in the article of Granger and Morris (1976) and by our earlier article (Ku and Seneta, 1998), to which the present article is a self-contained sequel. The theory is illustrated by the analysis of tree ring data.

Date: 2016
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DOI: 10.1080/03610926.2014.904349

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