Properties of the neural network sieve bootstrap

Abstract

In this paper, a sieve bootstrap scheme, the neural network sieve bootstrap, for nonlinear time series is proposed. The approach, which is nonparametric in its spirit, retains the conceptual simplicity of a classical residual bootstrap, and it has some advantages with respect to the blockwise schemes and kernel bootstrap techniques. The resampling scheme from the residuals of the feedforward neural networks is shown to be asymptotically justified. A Monte Carlo simulation study shows that the procedure performs similar to the autoregressive (AR)-sieve bootstrap for linear processes, while it outperforms the AR-sieve bootstrap, the moving block bootstrap and kernel bootstrap for nonlinear processes, both in terms of bias and variability.

Keywords:

• neural networks
• sieve bootstrap
• nonlinear time series
• Monte Carlo

AMS Subject Classifications:

• 62F40
• 62M10
• 62M45