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Large and moderate deviations for infinite-dimensional autoregressive processes

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  • Mas, André
  • Menneteau, Ludovic

Abstract

We consider large and moderate deviations for the empirical mean and covariance of hilbertian autoregressive processes. As an application we obtain moderate deviations principles for the eigenvalues and associated projectors of the empirical covariance.

Suggested Citation

  • Mas, André & Menneteau, Ludovic, 2003. "Large and moderate deviations for infinite-dimensional autoregressive processes," Journal of Multivariate Analysis, Elsevier, vol. 87(2), pages 241-260, November.
    • Handle: RePEc:eee:jmvana:v:87:y:2003:i:2:p:241-260
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    References listed on IDEAS

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    1. Philippe C. Besse & Herve Cardot & David B. Stephenson, 2000. "Autoregressive Forecasting of Some Functional Climatic Variations," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(4), pages 673-687, December.
    2. Mas, André, 2002. "Weak convergence for the covariance operators of a Hilbertian linear process," Stochastic Processes and their Applications, Elsevier, vol. 99(1), pages 117-135, May.
    3. Chen, Xia, 1997. "Moderate deviations for m-dependent random variables with Banach space values," Statistics & Probability Letters, Elsevier, vol. 35(2), pages 123-134, September.
    4. Ruymgaart, Frits H. & Yang, Song, 1997. "Some Applications of Watson's Perturbation Approach to Random Matrices," Journal of Multivariate Analysis, Elsevier, vol. 60(1), pages 48-60, January.
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    Cited by:

    1. 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.
    2. Mas, André, 2007. "Weak convergence in the functional autoregressive model," Journal of Multivariate Analysis, Elsevier, vol. 98(6), pages 1231-1261, July.
    3. Claudio Macci & Stefano Trapani, 2013. "Large deviations for posterior distributions on the parameter of a multivariate $$\text{ AR}(p)$$ process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(4), pages 703-719, August.
    4. Yu, Miao & Si, Shen, 2009. "Moderate deviation principle for autoregressive processes," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 1952-1961, October.
    5. Chun Yip Yau & Zifeng Zhao, 2016. "Inference for multiple change points in time series via likelihood ratio scan statistics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(4), pages 895-916, September.
    6. Yu Miao & Yanling Wang & Guangyu Yang, 2015. "Moderate Deviation Principles for Empirical Covariance in the Neighbourhood of the Unit Root," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(1), pages 234-255, March.
    7. Álvarez-Liébana, J. & Bosq, D. & Ruiz-Medina, M.D., 2017. "Asymptotic properties of a component-wise ARH(1) plug-in predictor," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 12-34.
    8. Mao, Mingzhi, 2014. "The asymptotic behaviors for least square estimation of multi-casting autoregressive processes," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 110-124.
    9. 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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