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Oscillating Gaussian processes

Author

Listed:
  • Pauliina Ilmonen

    (Aalto University School of Science)

  • Soledad Torres

    (CIMFAV Universidad de Valparaíso)

  • Lauri Viitasaari

    (Aalto University School of Business)

Abstract

In this article we introduce and study oscillating Gaussian processes defined by $$X_t = \alpha _+ Y_t \mathbf{1}_{Y_t >0} + \alpha _- Y_t\mathbf{1}_{Y_t 0 + α - Y t 1 Y t 0$$ 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 $$L^p$$ L p and are, when suitably normalised, asymptotically normal.

Suggested Citation

  • Pauliina Ilmonen & Soledad Torres & Lauri Viitasaari, 2020. "Oscillating Gaussian processes," Statistical Inference for Stochastic Processes, Springer, vol. 23(3), pages 571-593, October.
    • Handle: RePEc:spr:sistpr:v:23:y:2020:i:3:d:10.1007_s11203-020-09212-6
    DOI: 10.1007/s11203-020-09212-6
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    References listed on IDEAS

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    1. Hu, Yaozhong & Nualart, David & Song, Xiaoming, 2008. "A singular stochastic differential equation driven by fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2075-2085, October.
    2. Mishura, Yu. & Nualart, D., 2004. "Weak solutions for stochastic differential equations with additive fractional noise," Statistics & Probability Letters, Elsevier, vol. 70(4), pages 253-261, December.
    3. Breuer, Péter & Major, Péter, 1983. "Central limit theorems for non-linear functionals of Gaussian fields," Journal of Multivariate Analysis, Elsevier, vol. 13(3), pages 425-441, September.
    4. Tommi Sottinen & Lauri Viitasaari, 2018. "Parameter estimation for the Langevin equation with stationary-increment Gaussian noise," Statistical Inference for Stochastic Processes, Springer, vol. 21(3), pages 569-601, October.
    5. Azmoodeh, Ehsan & Sottinen, Tommi & Viitasaari, Lauri & Yazigi, Adil, 2014. "Necessary and sufficient conditions for Hölder continuity of Gaussian processes," Statistics & Probability Letters, Elsevier, vol. 94(C), pages 230-235.
    6. Shuyang Bai & Murad S. Taqqu, 2013. "Multivariate Limit Theorems In The Context Of Long-Range Dependence," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(6), pages 717-743, November.
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    Cited by:

    1. Héctor Araya & Meryem Slaoui & Soledad Torres, 2022. "Bayesian inference for fractional Oscillating Brownian motion," Computational Statistics, Springer, vol. 37(2), pages 887-907, April.

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