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Nonparametric estimation of the kernel function of symmetric stable moving average random functions

Author

Listed:
  • Jürgen Kampf

    (University of Rostock)

  • Georgiy Shevchenko

    (Taras Shevchenko National University of Kiev)

  • Evgeny Spodarev

    (Ulm University)

Abstract

We estimate the kernel function of a symmetric alpha stable ( $$S\alpha S$$ S α S ) moving average random function which is observed on a regular grid of points. The proposed estimator relies on the empirical normalized (smoothed) periodogram. It is shown to be weakly consistent for positive definite kernel functions, when the grid mesh size tends to zero and at the same time the observation horizon tends to infinity (high-frequency observations). A simulation study shows that the estimator performs well at finite sample sizes, when the integrator measure of the moving average random function is $$S\alpha S$$ S α S and for some other infinitely divisible integrators.

Suggested Citation

  • Jürgen Kampf & Georgiy Shevchenko & Evgeny Spodarev, 2021. "Nonparametric estimation of the kernel function of symmetric stable moving average random functions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(2), pages 337-367, April.
    • Handle: RePEc:spr:aistmt:v:73:y:2021:i:2:d:10.1007_s10463-020-00751-6
    DOI: 10.1007/s10463-020-00751-6
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    References listed on IDEAS

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    1. Koblents, Eugenia & Míguez, Joaquín & Rodríguez, Marco A. & Schmidt, Alexandra M., 2016. "A nonlinear population Monte Carlo scheme for the Bayesian estimation of parameters of α-stable distributions," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 57-74.
    2. Vicky Fasen & Florian Fuchs, 2013. "Spectral estimates for high-frequency sampled continuous-time autoregressive moving average processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(5), pages 532-551, September.
    3. Joanna Janczura & Sebastian Orzel & Agnieszka Wylomanska, 2011. "Subordinated alpha-stable Ornstein-Uhlenbeck process as a tool for financial data description," HSC Research Reports HSC/11/03, Hugo Steinhaus Center, Wroclaw University of Technology.
    4. Müller, Gernot & Seibert, Armin, 2019. "Bayesian estimation of stable CARMA spot models for electricity prices," Energy Economics, Elsevier, vol. 78(C), pages 267-277.
    5. Peter J. Brockwell & Vincenzo Ferrazzano & Claudia Klüppelberg, 2013. "High-frequency sampling and kernel estimation for continuous-time moving average processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(3), pages 385-404, May.
    6. P. Brockwell, 2014. "Recent results in the theory and applications of CARMA processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(4), pages 647-685, August.
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