The autoregression bootstrap for kernel estimates of smooth nonlinear functional time series

Jürgen E. Franke, Johannes T. N. Krebs

Publication date: 14 November 2018

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.

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