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

Marko Voutilainen*, Lauri Viitasaari, Pauliina Ilmonen

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

3 Citations (Scopus)
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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.

Original languageEnglish
Pages (from-to)195-207
Number of pages13
JournalModern Stochastics: Theory and Applications
Issue number2
Publication statusPublished - Jun 2019
MoE publication typeA1 Journal article-refereed


  • AR(1)-characterisation
  • stationary processes
  • covariance functions

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