Strongly consistent autoregressive predictors in abstract Banach spaces

@article{RuizMedina2018StronglyCA,
  title={Strongly consistent autoregressive predictors in abstract Banach spaces},
  author={Mar{\'i}a Dolores Ruiz-Medina and Javier {\'A}lvarez-Li{\'e}bana},
  journal={J. Multivariate Analysis},
  year={2018},
  volume={170},
  pages={186-201}
}
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… CONTINUE READING
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