The autoregression bootstrap for kernel estimates of smooth nonlinear functional time series
Statistics Theory
2018-11-16 v1 Statistics Theory
Abstract
Functional times series have become an integral part of both functional data and time series analysis. This paper deals with the functional autoregressive model of order 1 and the autoregression bootstrap for smooth functions. The regression operator is estimated in the framework developed by Ferraty and Vieu [2004] and Ferraty et al. [2007] which is here extended to the double functional case under an assumption of stationary ergodic data which dates back to Laib and Louani [2010]. The main result of this article is the characterization of the asymptotic consistency of the bootstrapped regression operator.
Keywords
Cite
@article{arxiv.1811.06172,
title = {The autoregression bootstrap for kernel estimates of smooth nonlinear functional time series},
author = {Johannes T. N. Krebs and Jürgen E. Franke},
journal= {arXiv preprint arXiv:1811.06172},
year = {2018}
}