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LASSO estimation for spherical autoregressive processes

Author

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  • Caponera, Alessia
  • Durastanti, Claudio
  • Vidotto, Anna

Abstract

The purpose of the present paper is to investigate a class of spherical functional autoregressive processes in order to introduce and study LASSO (Least Absolute Shrinkage and Selection Operator) type estimators for the corresponding autoregressive kernels, defined in the harmonic domain by means of their spectral decompositions. Some crucial properties for these estimators are proved, in particular, consistency and oracle inequalities.

Suggested Citation

  • Caponera, Alessia & Durastanti, Claudio & Vidotto, Anna, 2021. "LASSO estimation for spherical autoregressive processes," Stochastic Processes and their Applications, Elsevier, vol. 137(C), pages 167-199.
    • Handle: RePEc:eee:spapps:v:137:y:2021:i:c:p:167-199
    DOI: 10.1016/j.spa.2021.03.009
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    References listed on IDEAS

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    1. Jun, Mikyoung, 2014. "Matérn-based nonstationary cross-covariance models for global processes," Journal of Multivariate Analysis, Elsevier, vol. 128(C), pages 134-146.
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    5. Song, Song & Bickel, Peter J., 2011. "Large vector auto regressions," SFB 649 Discussion Papers 2011-048, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    6. Emilio Porcu & Moreno Bevilacqua & Marc G. Genton, 2016. "Spatio-Temporal Covariance and Cross-Covariance Functions of the Great Circle Distance on a Sphere," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 888-898, April.
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    Cited by:

    1. Alessia Caponera, 2021. "SPHARMA approximations for stationary functional time series on the sphere," Statistical Inference for Stochastic Processes, Springer, vol. 24(3), pages 609-634, October.

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