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Joint asymptotics for estimating the fractal indices of bivariate Gaussian processes

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  • Zhou, Yuzhen
  • Xiao, Yimin

Abstract

Multivariate (or vector-valued) processes are important for modeling multiple variables. The fractal indices of the components of the underlying multivariate process play a key role in characterizing the dependence structures and statistical properties of the multivariate process. In this paper, under the infill asymptotics framework, we establish joint asymptotic results for the increment-based estimators of bivariate fractal indices. Our main results quantitatively describe the effect of the cross-dependence structure on the performance of the estimators.

Suggested Citation

  • Zhou, Yuzhen & Xiao, Yimin, 2018. "Joint asymptotics for estimating the fractal indices of bivariate Gaussian processes," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 56-72.
    • Handle: RePEc:eee:jmvana:v:165:y:2018:i:c:p:56-72
    DOI: 10.1016/j.jmva.2017.12.001
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    References listed on IDEAS

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    1. Gneiting, Tilmann & Kleiber, William & Schlather, Martin, 2010. "Matérn Cross-Covariance Functions for Multivariate Random Fields," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1167-1177.
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    5. Lim, Chae Young & Stein, Michael, 2008. "Properties of spatial cross-periodograms using fixed-domain asymptotics," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 1962-1984, October.
    6. Furrer, Reinhard & Bachoc, François & Du, Juan, 2016. "Asymptotic properties of multivariate tapering for estimation and prediction," Journal of Multivariate Analysis, Elsevier, vol. 149(C), pages 177-191.
    7. Kleiber, William & Nychka, Douglas, 2012. "Nonstationary modeling for multivariate spatial processes," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 76-91.
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    Cited by:

    1. Szarek, Dawid & Maraj-Zygmąt, Katarzyna & Sikora, Grzegorz & Krapf, Diego & Wyłomańska, Agnieszka, 2022. "Statistical test for anomalous diffusion based on empirical anomaly measure for Gaussian processes," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    2. Hong, Yiping & Zhou, Zaiying & Yang, Ying, 2020. "Hypothesis testing for the smoothness parameter of Matérn covariance model on a regular grid," Journal of Multivariate Analysis, Elsevier, vol. 177(C).

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