  We propose a parametrization of autoregressive unit roots ARMA models (ARUMA)
with partial autocorrelation coefficients to specify the autoregressive and
integrated part of the model. We obtain the algebraic properties of the partial
autocorrelations in the context of unit roots. The main result is that if a
partial autocorrelation sequence contains some values equal to 1 or -1, then it
can be split at these values into sub-sequences each of which represents the
partial autocorrelations of a factor of the overall polynomial on the left-hand
side of the model. A separate paper will discuss the details of the estimation
procedure and its properties. An implementation is provided by Boshnakov and
Halliday (2022) R package sarima, https://cran.r-project.org/package=sarima
(function sarima).
