Oscillating Gaussian processes

Pauliina Ilmonen, Soledad Torres, Lauri Viitasaari*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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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
JournalStatistical Inference for Stochastic Processes
Early online date1 Jan 2020
DOIs
Publication statusPublished - 29 Apr 2020
MoE publication typeA1 Journal article-refereed

Keywords

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

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