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Asymptotic behavior of mixed power variations and statistical estimation in mixed models

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  • Marco Dozzi
  • Yuliya Mishura
  • Georgiy Shevchenko

Abstract

We obtain results on both weak and almost sure asymptotic behaviour of power variations of a linear combination of independent Wiener process and fractional Brownian motion. These results are used to construct strongly consistent parameter estimators in mixed models. Copyright Springer Science+Business Media Dordrecht 2015

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  • Marco Dozzi & Yuliya Mishura & Georgiy Shevchenko, 2015. "Asymptotic behavior of mixed power variations and statistical estimation in mixed models," Statistical Inference for Stochastic Processes, Springer, vol. 18(2), pages 151-175, July.
    • Handle: RePEc:spr:sistpr:v:18:y:2015:i:2:p:151-175
    DOI: 10.1007/s11203-014-9106-5
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    References listed on IDEAS

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    1. Benassi, Albert & Cohen, Serge & Istas, Jacques, 1998. "Identifying the multifractional function of a Gaussian process," Statistics & Probability Letters, Elsevier, vol. 39(4), pages 337-345, August.
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    3. van Zanten, Harry, 2007. "When is a linear combination of independent fBm's equivalent to a single fBm?," Stochastic Processes and their Applications, Elsevier, vol. 117(1), pages 57-70, January.
    4. Jean-François Coeurjolly, 2001. "Estimating the Parameters of a Fractional Brownian Motion by Discrete Variations of its Sample Paths," Statistical Inference for Stochastic Processes, Springer, vol. 4(2), pages 199-227, May.
    5. Coeurjolly, Jean-Francois, 2000. "Simulation and identification of the fractional Brownian motion: a bibliographical and comparative study," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 5(i07).
    6. Jean‐Marc Bardet & Pierre Bertrand, 2007. "Identification of the multiscale fractional Brownian motion with biomechanical applications," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(1), pages 1-52, January.
    7. Bardet, Jean-Marc & Surgailis, Donatas, 2013. "Moment bounds and central limit theorems for Gaussian subordinated arrays," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 457-473.
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    Cited by:

    1. Alexander Kukush & Stanislav Lohvinenko & Yuliya Mishura & Kostiantyn Ralchenko, 2022. "Two approaches to consistent estimation of parameters of mixed fractional Brownian motion with trend," Statistical Inference for Stochastic Processes, Springer, vol. 25(1), pages 159-187, April.

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