Strongly consistent autoregressive predictors in abstract Banach spaces

María D. Ruiz-Medina and Javier Álvarez-Liébana

Journal of Multivariate Analysis, 2019, vol. 170, issue C, 186-201

Abstract: This work derives new results on strong consistent estimation and prediction for autoregressive processes of order 1 in a separable Banach space B. The consistency results are obtained for the component-wise estimator of the autocorrelation operator in the norm of the space L(B) of bounded linear operators on B. The strong consistency of the associated plug-in predictor then follows in the B-norm. A Gelfand triple is defined through the Hilbert space constructed in Kuelbs’ lemma (Kuelbs, 1970). A Hilbert–Schmidt embedding introduces the Reproducing Kernel Hilbert space (RKHS), generated by the autocovariance operator, into the Hilbert space conforming the Rigged Hilbert space structure. This paper extends the work of Bosq (2000) and Labbas and Mourid (2002).

Keywords: Banach spaces; Continuous embeddings; Functional plug-in predictors; Strongly consistent estimators (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:170:y:2019:i:c:p:186-201

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DOI: 10.1016/j.jmva.2018.08.001

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