  It was recently proved that any strictly stationary stochastic process can be
viewed as an autoregressive process of order one with coloured noise.
Furthermore, it was proved that, using this characterisation, one can define
closed form estimators for the model parameter based on autocovariance
estimators for several different lags. However, this estimation procedure may
fail in some special cases. In this article we provide a detailed analysis of
these special cases. In particular, we prove that these cases correspond to
degenerate processes.
