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Maximum-Likelihood Asymptotic Inference for Autoregressive Hilbertian Processes

Author

Listed:
  • M. D. Ruiz-Medina

    (Faculty of Sciences, University of Granada)

  • R. M. Espejo

    (University of Granada)

Abstract

The autoregressive Hilbertian process framework has been introduced in Bosq (2000). This book provides the nonparametric estimation of the autocorrelation and covariance operators of the autoregressive Hilbertian processes. The asymptotic properties of these estimators are also provided. The maximum likelihood approach still remains unexplored. This paper obtains the asymptotic distribution of the maximum likelihood (ML) estimators of the auto-covariance operator of the Hilbert-valued innovation process, and of the autocorrelation operator of a Gaussian autoregressive Hilbertian process of order one. A real data example is analyzed in the financial context for illustration of the performance of the projection maximum likelihood estimation methodology in the context of missing data.

Suggested Citation

  • M. D. Ruiz-Medina & R. M. Espejo, 2015. "Maximum-Likelihood Asymptotic Inference for Autoregressive Hilbertian Processes," Methodology and Computing in Applied Probability, Springer, vol. 17(1), pages 207-222, March.
    • Handle: RePEc:spr:metcap:v:17:y:2015:i:1:d:10.1007_s11009-013-9329-8
    DOI: 10.1007/s11009-013-9329-8
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    References listed on IDEAS

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    1. Ruiz-Medina, M.D., 2011. "Spatial autoregressive and moving average Hilbertian processes," Journal of Multivariate Analysis, Elsevier, vol. 102(2), pages 292-305, February.
    2. Serge Guillas & Ming-Jun Lai, 2010. "Bivariate splines for spatial functional regression models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(4), pages 477-497.
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