Note on AR(1)-characterisation of stationary processes and model fitting

Note on AR(1)-characterisation of stationary processes and model fitting

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It was recently proved that any strictly stationary stochastic process can be viewed 9021 glow 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 candy coated licorice pastels special cases.

In this article, a detailed analysis of these special cases is provided.In particular, it is proved that these cases correspond to degenerate processes.