We consider the challenge of detecting and clustering point and collective anomalies in streaming data that exhibit significant nonlinearities and seasonal structures. The challenge is motivated by detecting problems in a communications network, where we can measure the throughput of nodes, and wish to rapidly detect anomalous traffic behaviour. Our approach is to train a neural network-based nonlinear autoregressive exogenous model on initial training data, then to use the sequential collective and point anomaly framework to identify anomalies in the residuals generated by comparing one-step-ahead predictions of the fitted model with the observations, and finally, we cluster the detected anomalies with fuzzy c-means clustering using empirical cumulative distribution functions. The autoregressive model is sufficiently general and robust such that it provides the nearly (locally) stationary residuals required by the anomaly detection procedure. The combined methods are successfully implemented to create an adaptive, robust, computational framework that can be used to cluster point and collective anomalies in streaming data. We validate the method on both data from the core of the UK’s national communications network and the multivariate Skoltech anomaly benchmark and find that the proposed method succeeds in dealing with different forms of anomalies within the nonlinear signals and outperforms conventional methods for anomaly detection and clustering.