Clustering nonlinear time series with neural network bootstrap forecast distributions

A new method for clustering nonlinear time series data is proposed. It is based on the forecast distributions, which are estimated by using a feed-forward neural network and the pair bootstrap. The procedure is shown to deliver consistent results for pure autoregressive dependent structures. It is model-free within a general class of nonlinear autoregression processes, and it avoids the specification of a finite dimensional model for the data generating process. The results of a Monte Carlo study are reported in order to investigate the finite sample performances of the proposed time series clustering approach. An application to a real dataset of economic time series is also discussed.