Oscillating Gaussian processes

Pauliina Ilmonen; Soledad Torres; Lauri Viitasaari

doi:10.1007/s11203-020-09212-6

Oscillating Gaussian processes

Pauliina Ilmonen, Soledad Torres, Lauri Viitasaari^*

^*Corresponding author for this work

Universidad de Valparaíso

Research output: Contribution to journal › Article › Scientific › peer-review

3 Citations (Scopus)

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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 L^p and are, when suitably normalised, asymptotically normal.

Original language	English
Pages (from-to)	571-593
Number of pages	23
Journal	Statistical Inference for Stochastic Processes
Volume	23
Issue number	3
Early online date	1 Jan 2020
DOIs	https://doi.org/10.1007/s11203-020-09212-6
Publication status	Published - Oct 2020
MoE publication type	A1 Journal article-refereed

Keywords

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

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title = "Oscillating Gaussian processes",

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.",

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AU - Torres, Soledad

AU - Viitasaari, Lauri

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N2 - 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.

AB - 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.

KW - Central limit theorem

KW - Gaussian processes

KW - Oscillating processes

KW - Parameter estimation

KW - Self-similarity

KW - Stationarity

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M3 - Article

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JF - Statistical Inference for Stochastic Processes

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ER -

Oscillating Gaussian processes

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Keywords

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