Ruiz Medina, María DoloresÁlvarez Liébana, JavierVon Rosen, Dietrich2024-01-242024-01-242018Ruiz-Medina, M. D.; Álvarez-Liébana, J. Strongly consistent autoregressive predictors in abstract Banach spaces. Journal of Multivariate Analysis 2019, 170, 186–201. doi:10.1016/j.jmva.2018.08.001.0047-259X10.1016/j.jmva.2018.08.001https://hdl.handle.net/20.500.14352/95141Supplementary Material to "Strongly-consistent autoregressive predictors in abstract Banach spaces": https://ars-els-cdn-com.bucm.idm.oclc.org/content/image/1-s2.0-S0047259X17307248-mmc1.pdfThis 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).engAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/journal articlehttps://doi.org/10.1016/j.jmva.2018.08.001https://www-sciencedirect-com.bucm.idm.oclc.org/science/article/pii/S0047259X17307248https://www-sciencedirect-com.bucm.idm.oclc.org/journal/journal-of-multivariate-analysisrestricted access519.246.8330.1Banach spacesContinuous embeddingsFunctional plug-in predictorsStrongly consistent estimatorsAnálisis funcional y teoría de operadoresEconometría (Estadística)1202 Análisis y Análisis Funcional5302 Econometría