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

Kare Kamila ()
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Kare Kamila: SAMM, Université Paris 1, Panthéon-Sorbonne

Annals of the Institute of Statistical Mathematics, 2023, vol. 75, issue 4, No 2, 567-592

Abstract: 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 .

Keywords: Model selection; Oracle inequality; Efficiency; Autoregressive process; Data driven (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10463-022-00855-1

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