|This paper proposes and discusses a new procedure to estimate the forecast distribution for nonlinear autoregressive time series. The approach employs a feed-forward neural network estimated using extreme learning machines (ELMs) to approximate the original nonlinear process and the pair bootstrap as a resampling device. Compared with conventional neural network algorithms, ELMs have substantial advantages such as fast learning speed and ease of implementation. Moreover, they are particularly useful in all cases which require real-time retraining of the network, significantly reducing the computational problems of the bootstrap procedure. The proposed approach is instrumental in all applications where time series should be longer to justify using complex neural network models, such as LSTM or other deep learning approaches. This is the case, for example, of economic time series, where it is rare to find time series longer than a few hundred-time points. The results of a Monte Carlo simulation experiment show that ELMs can significantly reduce the computational burden of the overall procedure while preserving the good accuracy of completely tuned neural networks.
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