Oscillating Gaussian processes

Pauliina Ilmonen, Soledad Torres, Lauri Viitasaari*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)
24 Downloads (Pure)

Abstract

In this article we introduce and study oscillating Gaussian processes defined by Xt=α+Yt1Yt>0+α-Yt1Yt<0, where α+, α-> 0 are free parameters and Y is either stationary or self-similar Gaussian process. We study the basic properties of X and we consider estimation of the model parameters. In particular, we show that the moment estimators converge in Lp and are, when suitably normalised, asymptotically normal.

Original languageEnglish
Pages (from-to)571-593
Number of pages23
JournalStatistical Inference for Stochastic Processes
Volume23
Issue number3
Early online date1 Jan 2020
DOIs
Publication statusPublished - Oct 2020
MoE publication typeA1 Journal article-refereed

Keywords

  • Central limit theorem
  • Gaussian processes
  • Oscillating processes
  • Parameter estimation
  • Self-similarity
  • Stationarity

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