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 as an autoregressive process 15-eg2373cl of order one with coloured noise.Furthermore, it was proved that, using this characterisation, one can define closed form estimators for the model parameter click here based on autocovariance estimators for several different lags.However, this estimation procedure may fail in some 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.