Note on AR(1)-characterisation of stationary processes and model fitting
Volume 6, Issue 2 (2019), pp. 195–207
Pub. online: 8 March 2019
Type: Research Article
Open Access
Open Access
Received
5 October 2018
5 October 2018
Revised
13 February 2019
13 February 2019
Accepted
13 February 2019
13 February 2019
Published
8 March 2019
8 March 2019
Abstract
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, a detailed analysis of these special cases is provided. In particular, it is proved that these cases correspond to degenerate processes.
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