Non-linear time series clustering based on non-parametric forecast densities

The problem of clustering time series is studied for a general class of non-parametric autoregressive models. The dissimilarity between two time series is based on comparing their full forecast densities at a given horizon. In particular, two functional distances are considered: L1 and L2. As the forecast densities are unknown, they are approximated using a bootstrap procedure that mimics the underlying generating processes without assuming any parametric model for the true autoregressive structure of the series. The estimated forecast densities are then used to construct the dissimilarity matrix and hence to perform clustering. Asymptotic properties of the proposed method are provided and an extensive simulation study is carried out. The results show the good behavior of the procedure for a wide variety of nonlinear autoregressive models and its robustness to non-Gaussian innovations. Finally, the proposed methodology is applied to a real dataset involving economic time series.