A uniform central limit theorem for neural network-based autoregressive processes with applications to change-point analysis

Abstract

We consider an autoregressive process with a nonlinear regression function that is modelled by a feedforward neural network. First, we derive a uniform central limit theorem which is useful in the context of change-point analysis. Then, we propose a test for a change in the autoregression function which – by the uniform central limit theorem – has asymptotic power one for a large class of alternatives including local alternatives not restricted to the correctly specified model.

Keywords:

• uniform central limit theorem
• nonparametric regression
• neural network
• autoregressive process

AMS Subject Classification:

• 60F05
• 62J02
• 62M45

Acknowledgements

The work was supported by the DFG graduate college ‘Mathematics and Practice’ as well as by the DFG grants KI 1443/2-1 and KI 1443/2-2. The position of the first author was financed by the Stifterverband für die Deutsche Wissenschaft by funds of the Claussen–Simon-trust.