On model fitting and estimation of strictly stationary processes

Marko Voutilainen, Lauri Viitasaari, Pauliina Ilmonen

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Stationary processes have been extensively studied in the literature. Their applications include modeling and forecasting numerous real life phenomena such as natural disasters, sales and market movements. When stationary processes are considered, modeling is traditionally based on fitting an autoregressive moving average (ARMA) process. However, we challenge this conventional approach. Instead of fitting an ARMA model, we apply an AR(1) characterization in modeling any strictly stationary processes. Moreover, we derive consistent and asymptotically normal estimators of the corresponding model parameter.
Original languageEnglish
Pages (from-to)381-406
JournalModern Stochastics: Theory and Applications
Issue number4
Publication statusPublished - 2017
MoE publication typeA1 Journal article-refereed


  • representation
  • asymptotic normality
  • consistency
  • estimation
  • strictly stationary processes


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