Nonlinear autoregressive sieve bootstrap based on extreme learning machines.

The aim of the paper is to propose and discuss a sieve bootstrap scheme based on Extreme Learning Machines for non linear time series. The procedure is fully nonparametric in its spirit and retains the conceptual simplicity of the residual bootstrap. Using Extreme Learning Machines in the resampling scheme can dramatically reduce the computational burden of the bootstrap procedure, with performances comparable to the NN-Sieve bootstrap and computing time similar to the ARSieve bootstrap. A Monte Carlo simulation experiment has been implemented, in order to evaluate the performance of the proposed procedure and to compare it with the NN-Sieve bootstrap. The distributions of the bootstrap variance estimators appear to be consistent, delivering good results both in terms of accuracy and bias, for either linear and nonlinear statistics (such as the mean and the median) and smooth functions of means (such as the variance and the covariance).