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Estimation of Mean and Covariance Operator of Autoregressive Processes in Banach Spaces

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  • Denis Bosq

Abstract

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Suggested Citation

  • Denis Bosq, 2002. "Estimation of Mean and Covariance Operator of Autoregressive Processes in Banach Spaces," Statistical Inference for Stochastic Processes, Springer, vol. 5(3), pages 287-306, October.
    • Handle: RePEc:spr:sistpr:v:5:y:2002:i:3:p:287-306
    DOI: 10.1023/A:1021279131053
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    Citations

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    Cited by:

    1. Axel Bücher & Holger Dette & Florian Heinrichs, 2020. "Detecting deviations from second-order stationarity in locally stationary functional time series," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(4), pages 1055-1094, August.
    2. 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.
    3. Horta, Eduardo & Ziegelmann, Flavio, 2018. "Conjugate processes: Theory and application to risk forecasting," Stochastic Processes and their Applications, Elsevier, vol. 128(3), pages 727-755.
    4. Panaretos, Victor M. & Tavakoli, Shahin, 2013. "Cramér–Karhunen–Loève representation and harmonic principal component analysis of functional time series," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2779-2807.
    5. Ruiz-Medina, María D. & Álvarez-Liébana, Javier, 2019. "Strongly consistent autoregressive predictors in abstract Banach spaces," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 186-201.
    6. Álvarez-Liébana, Javier & Bosq, Denis & Ruiz-Medina, María D., 2016. "Consistency of the plug-in functional predictor of the Ornstein–Uhlenbeck process in Hilbert and Banach spaces," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 12-22.
    7. van Delft, Anne, 2020. "A note on quadratic forms of stationary functional time series under mild conditions," Stochastic Processes and their Applications, Elsevier, vol. 130(7), pages 4206-4251.
    8. Aneiros, Germán & Cao, Ricardo & Fraiman, Ricardo & Genest, Christian & Vieu, Philippe, 2019. "Recent advances in functional data analysis and high-dimensional statistics," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 3-9.
    9. van Delft, Anne & Eichler, Michael, 2017. "Locally Stationary Functional Time Series," LIDAM Discussion Papers ISBA 2017023, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    10. Menneteau, Ludovic, 2005. "Some laws of the iterated logarithm in Hilbertian autoregressive models," Journal of Multivariate Analysis, Elsevier, vol. 92(2), pages 405-425, February.

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