A residual-based bootstrap for functional autoregressions

Jürgen Franke; Euna Gesare Nyarige

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arXiv · 1905.07635

A residual-based bootstrap for functional autoregressions

Jürgen Franke·Euna Gesare Nyarige

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Abstract

We consider the residual-based or naive bootstrap for functional autoregressions of order 1 and prove that it is asymptotically valid for, e.g., the sample mean and for empirical covariance operator estimates. As a crucial auxiliary result, we also show that the empirical distribution of the centered sample innovations converges to the distribution of the innovations with respect to the Mallows metric.

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Jürgen Franke, Euna Gesare Nyarige. 2019-05-18. A residual-based bootstrap for functional autoregressions. https://arxiv.org/abs/1905.07635

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