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Data-driven model selection for same-realization predictions in autoregressive processes

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  • Kare Kamila

    (SAMM, Université Paris 1, Panthéon-Sorbonne)

Abstract

This paper is about the one-step ahead prediction of the future of observations drawn from an infinite-order autoregressive AR( $$\infty $$ ∞ ) process. It aims to design penalties (fully data driven) ensuring that the selected model verifies the efficiency property but in the non-asymptotic framework. We show that the excess risk of the selected estimator enjoys the best bias-variance trade-off over the considered collection. To achieve these results, we needed to overcome the dependence difficulties by following a classical approach which consists in restricting to a set where the empirical covariance matrix is equivalent to the theoretical one. We show that this event happens with probability larger than $$1-c_0/n^2$$ 1 - c 0 / n 2 with $$c_0>0$$ c 0 > 0 . The proposed data-driven criteria are based on the minimization of the penalized criterion akin to the Mallows’s $$C_p$$ C p .

Suggested Citation

  • Kare Kamila, 2023. "Data-driven model selection for same-realization predictions in autoregressive processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(4), pages 567-592, August.
    • Handle: RePEc:spr:aistmt:v:75:y:2023:i:4:d:10.1007_s10463-022-00855-1
    DOI: 10.1007/s10463-022-00855-1
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    References listed on IDEAS

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    1. Doukhan, Paul & Wintenberger, Olivier, 2008. "Weakly dependent chains with infinite memory," Stochastic Processes and their Applications, Elsevier, vol. 118(11), pages 1997-2013, November.
    2. Ing, Ching-Kang & Wei, Ching-Zong, 2003. "On same-realization prediction in an infinite-order autoregressive process," Journal of Multivariate Analysis, Elsevier, vol. 85(1), pages 130-155, April.
    3. F. Comte & V. Genon-Catalot, 2020. "Regression function estimation as a partly inverse problem," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(4), pages 1023-1054, August.
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